Index

application of: Orthogonality, Reality, and Uniqueness

adjoint boundary conditions

Adjoint Boundary Conditions to Adjoint Boundary Conditions | 3. Apply Green's Identity

for a second order operator: Second Order Operator and

adjoint boundary value problem in 2 dimensions

adjoint eigenvalue problem

The Simple String and

adjoint of an operator

The Adjoint of an | The Simple String and | 2. Determine Green's Identity

advanced time

algorithm

pyramid: The Pyramid Algorithm to The Pyramid Algorithm

antilinear

Approximation via Subspaces: Analysis to Approximation via Subspaces: Analysis

appriximation via subspaces

Aristotle

The Fourier Transform as | The Fourier Transform as

auto correlation function

Ayn Rand

Boundary Value Problems in

Banach space

Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric

basis

optimal: Chirped Signals and the

beauty of mathematics

Approximation via Subspaces: Analysis | Approximation via Subspaces: Analysis | Approximation via Subspaces: Analysis

Bessel function

of order zero: 3. Apply Green's Identity

Bessel functions

orthonormalized: Orthogonality, Reality, and Uniqueness

Bessel's inequality

bilinear concomitant

vectorial: 2. Determine Green's Identity

Born approximation

Born series

boundary conditions

Cauchy

in two dimentions: Boundary Conditions of a

compatibility between

Homogeneous Boundary Conditions to Homogeneous Boundary Conditions

Dirichlet

in one dimension: The Homogeneous Problem
in two dimentions: Boundary Conditions of a

homogeneous

in two dimensions

Boundary Conditions of a to Boundary Conditions of a

mixed Dirichlet and Neuman

The Homogeneous Problem

mixed Dirichlet and Neumann

Construction of the Green's

Neumann

in one dimension: The Homogeneous Problem
in two dimentions: Boundary Conditions of a

periodic

The Homogeneous Problem

phase formulation of

The Boundary Conditions to The Boundary Conditions

three important types of

Boundary Conditions of a

boundary value problem

for a cavity: Finite Interior Boundary Value to Finite Interior Boundary Value
exterior: One-dimensional Scattering Problem: Exterior | Exterior Boundary Value Problem: to Exterior Boundary Value Problem:
via Green's function: Boundary Value Problem via
homogeneous: The Homogeneous Problem
inhomogeneous: The Totally Inhomogeneous Boundary
via integral equation: Boundary Value Problem via
interior: One-dimensional Cavity Problem: Interior
interior and finite: Finite Interior Boundary Value to Finite Interior Boundary Value
interior and infinite: Infinite Interior Boundary Value to Infinite Interior Boundary Value

branch cut

Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,

coalescence of poles: Coalescence of Poles into
integration around: Contour Integration Around the

branch of a function

Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,

Cauchy completeness

Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric

Cauchy completion

of an inner product spacef: Cauchy Completeness: Complete Metric
of a normed linear space: Cauchy Completeness: Complete Metric
of the rationals: Cauchy Completeness: Complete Metric

Cauchy conditions

see initial value conditions

Cauchy data

see initial value data

Cauchy incomplete

Cauchy Completeness: Complete Metric

Cauchy sequence

Cauchy Sequence to Cauchy Sequence

Cauchy-Schwarz inequality

central approximation space

Central Approximation Space | Unit-Economy via the Two | Unit-Economy via the Two

central space

see central approximation space

characteristic coordinates

characteristics

discontinuity across: Hyperbolic Equations | Hyperbolic Equations

characteristics of a hyperbolic equation

Chebyshev distance

chirped signals

Chirped Signals and the

commuting operators

complete set of: Special Function Theory | Complete Set of Commuting | Complete Set of Commuting to Complete Set of Commuting | Factorization Method for Solving

compatibility condition between boundary conditions

Complete Metric Spaces to Cauchy Completeness: Complete Metric

complete metric space

complete set

Recapitulation

complete set of commuting operators

Complete Set of Commuting to Complete Set of Commuting

complete set of orthonormal functions

Recapitulation

completeness

Completeness

criterion for: Completeness via Green's function

completeness of a set of S-L eigenfunctions

Completeness of the Set to Completeness of the Set | Completeness

completeness relation

completeness via Green's function

Completeness via Green's function | Completeness

complexity of mathematics

conjunct

convolution

Infinite Interior Boundary Value

applied to a translation invariant system: Translation Invariant Systems

critical frequency

cross correlation function

The Fourier Transform as

cylinder harmonic

as a superposition of plane waves: Wanted: Rotation Invariant Solutions | Properties of Hankel and

cylinder waves

see cylinder harmonics

cylindrical cavity

wave equation for a: Finite Interior Boundary Value to Finite Interior Boundary Value

degenerate eigenvalue

Special Function Theory | Degenerate Eigenvalues

degrees of freedom

The Dirac Delta Function to The Dirac Delta Function

differential equation

key principle for solving: The Homogeneous Problem
for Prüfer's phase: The Prüfer System
for Prüfer's amplitude: The Prüfer System
qualitative behaviour of its solutions: Qualitative Results to Qualitative Results
second solution to: Orthogonality, Reality, and Uniqueness

dipole

field: Static Multipole Field
moment: Static Multipole Field

Dirac delta function

Dirichelet basis

Dirichlet kernel

The Dirichlet Kernel

its basic properties: Basic Properties

distance

Chebyshev: Normed Linear Spaces
Hamming: Normed Linear Spaces
Pythagorean: Normed Linear Spaces

distance function

domain of dependence

doubly degenerate eigenvalues

dual basis

Duality Principle

duality relationship

effectiveness of mathematics

Approximation via Subspaces: Analysis

eigenfunctions

via an integral equation: Eigenfunctions via Integral Equations
even and odd: Orthogonality, Reality, and Uniqueness
normalization of: Orthogonality, Reality, and Uniqueness
unique: Orthogonality, Reality, and Uniqueness
uniqueness of: Orthogonality, Reality, and Uniqueness

eigenvalues

discrete and unbounded sequence of: Discrete Unbounded Sequence of to Discrete Unbounded Sequence of
doubly degenerate: Orthogonality, Reality, and Uniqueness
nondegenerate: Orthogonality, Reality, and Uniqueness
simple: Orthogonality, Reality, and Uniqueness

error vector

Euclidean plane

Helmholtz equation in the: The Helmholtz Equation to Wanted: Rotation Invariant Solutions
rotations in the: Translations and Rotations in | Translations and Rotations in to Translations and Rotations in
symmetry transformations of the: Translations and Rotations in
translations in the: Translations and Rotations in | Translations and Rotations in to Translations and Rotations in

evanescent wave

Infinite Interior Boundary Value

exterior boundary value problem

Translation Invariant Systems

factorization method

applied to Laplacian on a two-sphere: Factorization Method for Solving to Factorization Method for Solving
applied to Laplacian on the Euclidean plane: Properties of Hankel and to Properties of Hankel and
for solving Helmholtz's equation on a two-sphere: Factorization Method for Solving to Factorization Method for Solving
for solving Helmholtz's equation on the Euclidean plane: Properties of Hankel and to Properties of Hankel and

father wavelet

see scaling function

filter function

first Born approximation

Adjoint Boundary Conditions

formal adjoint of an operator

Fourier integral

The Fourier Integral to Efficient Calculation: Fourier Transform

Fourier series

Fourier Series of a

Fourier series theorem

Fourier Series of a

Fourier sine theorem

Fourier Sine Theorem

Fourier theory

Fourier Theory to Wavelet Analysis

Fourier transform

basic properties of: Fourier Transform via Parseval's
via convolution: Efficient Calculation: Fourier Transform
eigenfunctions of the: Orthogonality, Reality, and Uniqueness
eigenvalues of the: The Fourier Transform as
of generalized functions: Fourier Transform via Parseval's
as an isomorphism: The Fourier Transform as
of light from a mode-locked laser: Efficient Calculation: Fourier Transform
of an optical pulse train: Efficient Calculation: Fourier Transform | Efficient Calculation: Fourier Transform
via Parceval's relation: Fourier Transform via Parseval's to Fourier Transform via Parseval's
of a periodic function: Fourier Transform via Parseval's
of a periodic train of Gaussians: Efficient Calculation: Fourier Transform
its robustness: Fourier Transform via Parseval's
of a ticking clock: Fourier Transform via Parseval's
and tranlation invariance: The Fourier Integral
and translation invariant systems: Translation Invariant Systems
as a unitary transformation in $L^2(-\infty ,\infty )$: The Fourier Transform as
windowed: Isomorphic Hilbert Spaces

Fourier-Bessel series

Solution to Wave Equation | Solution to Wave Equation

Fraunhofer approximation

Fraunhofer-Kirchhoff theorem

Solution to Wave Equation

Fredholm alternative

Properties and Utility of

Fresnel approximation

Solution to Wave Equation

Fundamental theorem for Green's functions

Properties and Utility of

Gaussians

periodic train of: Efficient Calculation: Fourier Transform

generating functions

Properties of Hankel and

Green's function

acausal: Unit Impulse Response: General
adjoint of a: Green's Function and Its to Green's Function and Its
advanced: Unit Impulse Response: General
for the Bessel operator: The Simple String and
causal: Unit Impulse Response: General
construction of: Construction of the Green's to Construction of the Green's | Green's Function
continuity condition for the 1-dimensional: Point Force Applied to
for a vibrating string: String with Free Ends:
formula for a: Construction of the Green's
fundamental theorem for a: Properties and Utility of
for general homogeneous boundary conditions: Unit Impulse Response: General
initial conditions for: Unit Impulse Response: General | Unit Impulse Response: General
jump condition for the 1-dimensional: Point Force Applied to
pictorial definition: Pictorial Definition of a to Point Force Applied to
poles of a: Spectral Representation
properties and utility: Properties and Utility of to Properties and Utility of
reciprocity relation: Green's Function and Its
retarded: Unit Impulse Response: General
self-adjoint: Green's Function and Its
spectral representation: Spectral Representation to Completeness
spectrum via: Spectrum via Green's Function
for a static string: Construction of the Green's
for a translation invariant system: Translation Invariant Systems
uniqueness of: Properties and Utility of

Green's function problem

Introduction

Green's function theory

Green's Function Theory to Fourier Sine Theorem

Green's identity

adapted to a given differential operator in 2 dimensions: 2. Determine Green's Identity
in one dimension: Orthogonality, Reality, and Uniqueness
in three dimension: Orthogonality, Reality, and Uniqueness

Hamming distance

The Helmholtz Equation to Wanted: Rotation Invariant Solutions

Hankel functions

applications of: Exterior Boundary Value Problem: to Infinite Interior Boundary Value
properties of: Properties of Hankel and to Properties of Hankel and | More Properties of Hankel to More Properties of Hankel

heat conduction in 1 dimension

temperature profile for: Homogeneous Boundary Conditions

Helmholtz equation

solution to, in three dimensions: Solution to Wave Equation
in three dimensions: Solution to Wave Equation

Hermetian operator

The Adjoint of an

Hermite-Gauss polynomials

Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric

Hermitian adjoint

The Adjoint of an

Hilbert space

of square integrable functions: Two Prototypical Examples
of square summable sequences: Two Prototypical Examples

hyperbolic differential equation

Hyperbolic Equations to 3. Apply Green's Identity

integration via Riemann's method: Riemann's Method for Integrating to 3. Apply Green's Identity

infinite dimensional vector spaces

Infinite Dimensional Vector Spaces to Isomorphic Hilbert Spaces

infinite string

Infinite String to Infinite String

as the limit of a finite string: Infinite String as the to Infinite String as the

initial value conditions

Boundary Conditions of a

initial value data

Boundary Conditions of a | Hyperbolic Equations | 3. Apply Green's Identity

initial value problem

inner product norm

inner product space

integral equation

Boundary Value Problem via to Types of Integral Equations

eigenfunctions via: Eigenfunctions via Integral Equations

integral equations

of the first kind: Types of Integral Equations | Types of Integral Equations
Fredholm -: Types of Integral Equations
of the second kind: Types of Integral Equations | Types of Integral Equations
types of: Types of Integral Equations to Types of Integral Equations
Volterra -: Types of Integral Equations

interior boundary value problem

One-dimensional Cavity Problem: Interior

invariant subspace

Complete Set of Commuting

isometric transformation

Isomorphic Hilbert Spaces

isometry

Isomorphic Hilbert Spaces | The Fourier Transform as

isomorphic Hilbert spaces

Isomorphic Hilbert Spaces to Isomorphic Hilbert Spaces

isomorphism

Isomorphic Hilbert Spaces

Klein-Gordon wave equation

Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem | 2. Determine Green's Identity

Lagrange's identity

extension to two-dimensional domain: 2. Determine Green's Identity

laser

mode-locked: Efficient Calculation: Fourier Transform
phase-locked: Efficient Calculation: Fourier Transform

least squares approximation

Approximation via Subspaces: Analysis | The Dirichlet Kernel

Legendre polynomials

orthogonality of: Orthogonality, Reality, and Uniqueness

Legendre's equation

Factorization Method for Solving | The Bessel-Legendre Connection

its relation to Bessel's equation: The Bessel-Legendre Connection

``light bullets''

Properties of Hankel and | Factorization Method for Solving

linear algebra

archetypical problems: Introduction

logic

father of: Preface

lowering operator

magnetic dipole moment

Electromagnetic Fields in a

magnetic moment density

Electromagnetic Fields in a

magnetization

see magnetic moment density

Mallat, Stephane G.

Fourier Series of a | The Pyramid Algorithm

matched filter

The Fourier Transform as

mathematics

System of Partial Differential

as neither intrinsic nor subjective: Preface
basis of: Preface
beauty of: Preface
definition of: Preface
effectiveness of: Preface
its complexity: Preface
nature of: Preface to Preface
power of: Preface
theoretical vs. ``pure'': Preface

Maxwell's equations

how to solve them

System of Partial Differential to The TEM Field

in cylindrical coordinates: The TE Field to The TEM Field

mean frequency

Four Properties

mean position

Four Properties

mean squared error

Approximation via Subspaces: Analysis

metric space

Metric Spaces to Metric Spaces

complete: Complete Metric Spaces to Cauchy Completeness: Complete Metric
definition of: Metric Spaces
metric of: Metric Spaces

mode-locked laser

Construction and Properties

moment

dipole: Static Multipole Field
monopole: Static Multipole Field
quadrupole: Static Multipole Field

monopole

field: Static Multipole Field
moment: Static Multipole Field

mother wavelet

MRA

see multiresolution analysis

MSA

see multiscale analysis

MSA vs MRA

Multiscale Analysis vs Multiresolution

multiple scattering

Multiresolution Analysis | Unit-Economy via the Two | Multiscale Analysis vs Multiresolution

multipole

field: Static Multipole Field
moment: Static Multipole Field

multipole field

Static Multipole Field to Static Multipole Field

multiresolution analysis

multiscale analysis

Unit-Economy via the Two | Multiscale Analysis vs Multiresolution

nondegenerate eigenvalues

Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness

nonessential properties

see essential properties

normal forms

three types of: Cauchy Problem and Characteristics

normal mode

energy residing in each: Orthogonality, Reality, and Uniqueness
spatial amplitude profile for: Sturm-Liouville Differential Equation

normed linear spaces

null coordinates

see characteristic coordinates

optical pulse train

Orthonormal Wave Packet Representation to Phase Space Representation

Fourier transform of: Efficient Calculation: Fourier Transform | Efficient Calculation: Fourier Transform

optimal basis

Chirped Signals and the

orthogonal eigenfunctions

definition: Orthogonality, Reality, and Uniqueness

orthonormal wave packets

definition and properties: Orthonormal Wave Packets: Definition to Whittaker-Shannon Sampling Theorem: The
frequency spread: Four Properties
general construction: Orthonormal Wave Packets: General to Orthonormal Wave Packets: General
mean frequency: Four Properties
mean position: Four Properties
phase space representation: Phase Space Representation to Phase Space Representation
sifting property: Four Properties
temporal spread: Four Properties

orthonormal wavelet representation

Orthonormal Wavelet Representation to Construction and Properties

orthonormal wavelets

construction and properties: Construction and Properties to Construction and Properties

orthonormality

as an expression of energy conservation in each normal mode: Orthogonality, Reality, and Uniqueness

oscillation theorem

The Behavior of the to The Behavior of the

outgoing

wave: Exterior Boundary Value Problem:

parity operator

Single Partial Differential Equations: to 3. Apply Green's Identity

Parseval's relation

Approximation via Subspaces: Analysis | Recapitulation | Isomorphic Hilbert Spaces

partial differential equations

classification of: Cauchy Problem and Characteristics
three types of: Single Partial Differential Equations: | Cauchy Problem and Characteristics

partial Fourier sum

Fourier Series of a

periodic function

as a convolution: Efficient Calculation: Fourier Transform
Fourier transform of: Fourier Transform via Parseval's

phase analysis

Phase Analysis of a to Discrete Unbounded Sequence of

phase space

partitioning of: Phase Space Representation | Central Approximation Space | Central Approximation Space | Resolution Analysis as a | Resolution Analysis as a | Resolution Analysis as a | Resolution Analysis as a

phase space cells

Phase Space Representation

phase space representation

Phase Space Representation to Phase Space Representation

phase-coherent pulses

plane wave

as a superposition of cylinder waves: Properties of Hankel and to Properties of Hankel and

Poincaré phase plane

The Prüfer System | The Prüfer System | The Prüfer System

point transformations

Poisson's equation

The Simple String and

Poisson's summation formula

Fourier Series of a | Fourier Series of a

alternate form of: Fourier Series of a

positive definite

power of mathematics

Prüfer

amplitude: The Prüfer System
phase: The Prüfer System
substitution: The Prüfer System
system: The Prüfer System | The Prüfer System to Qualitative Results

principle of unit-economy

Chirped Signals and the | Unit-Economy via the Two | Partial Differential Equations

``pure'' mathematics as an invalid notion

Approximation via Subspaces: Analysis

pyramid algorithm

The Pyramid Algorithm to The Pyramid Algorithm

Pythagoras' theorem

Pythagorean distance

Properties of Hankel and | Factorization Method for Solving

quadrupole

field: Static Multipole Field
moment: Static Multipole Field

raising operator

Rand, Ayn

Boundary Value Problems in

Rayleigh quotient

Completeness of the Set

reciprocity relation

Green's Function and Its

reconstruction problem

Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem

regular S-L problem

resolution analysis

see also wavelet analysis | Resolution Analysis as a

resolution spaces

Resolution Spaces as Hierarchical

resolvent

Spectral Resolution of the

of an operator: Spectral Resolution of the

retarded time

Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,

Riemann sheets

Riemann's method for integrating a hyperbolic equation

Riemann's Method for Integrating to 3. Apply Green's Identity

Riemann's representation of a solution to a hyperbolic equation

The Riesz-Fischer Theorem | Subspace Approximation vs. the

Riemann-Lebesgue lemma

Fourier Series of a | Fourier Series of a | The Fourier Integral Theorem

Riesz basis

Central Approximation Space | Unit-Economy via the Two | Unit-Economy via the Two

Riesz-Fischer theorem

rotation eigenfunction

Wanted: Rotation Invariant Solutions

rotation generator

rotation operator

Central Approximation Space | Resolution Spaces as Hierarchical | The Scaling Function as

scaling equation

The Scaling Function as

scaling function

scattered wave

Exterior Boundary Value Problem:

scattering

multiple: One-dimensional Scattering Problem: Exterior

scattering problem

Exterior Boundary Value Problem: to Exterior Boundary Value Problem:

scattering process

Central Approximation Space | Translation Followed by Compression

self-adjoint

Green's function: Green's Function and Its
operator: Adjoint Boundary Conditions

Shannon basis

Shannon's sampling functions

Isomorphic Hilbert Spaces

sifting property

Phase Space Representation

simple string

The Simple String and

sinc function

singular S-L problem

Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem

special function theory

Special Function Theory to The Bessel-Legendre Connection

spectral representation

of a Green's function: Spectral Representation to Completeness
of the identity: Recapitulation | Spectral Resolution of the
of a Green's function: Spectral Representation
of the Dirac delta function: Spectral Representation of the
of an operator: Spectral Resolution of the
of a resolvent: Spectral Resolution of the

Spectrum via Green's function

Spectrum via Green's Function

spherical harmonics

Factorization Method for Solving to Factorization Method for Solving

addition theorem for: Additional Theorem for Spherical to Additional Theorem for Spherical
their relation to cylinder harmonics: The Bessel-Legendre Connection to The Bessel-Legendre Connection

spherically symmetric solutions

Spherically Symmetric Solutions to Spherically Symmetric Solutions

spherically symmetric systems, wave equation for

Wave Equation for Spherically to Wave Equation for Spherically

square integrability

Square Integrability to Square Integrability

square integrable functions

Two Prototypical Examples

square summable sequence

Two Prototypical Examples

steepest descent and stationary phase, the method of

The Method of Steepest to The Method of Steepest

string

imbedded in an elastic medium: Sturm-Liouville Differential Equation | 3. Apply Green's Identity
static: Construction of the Green's
with free ends: String with Free Ends: to Completeness

Sturm's comparison theorem

Sturm's Comparison Theorem to Sturm's Comparison Theorem

Sturm-Liouville

differential equation

Sturm-Liouville Differential Equation to Sturm-Liouville Differential Equation

eigenvalue problem

Basic Properties of a to Sturm's Comparison Theorem

periodic: Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
reality of its eigenvalues: Orthogonality, Reality, and Uniqueness
regular: Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
singular: Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
unique solution to: Orthogonality, Reality, and Uniqueness
uniqueness theorem for eigenfunctions: Orthogonality, Reality, and Uniqueness

systems

Sturm-Liouville Systems to Sturm's Comparison Theorem

completeness of their sets of eigenfunctions: Completeness of the Set to Completeness of the Set
meaning of: Basic Properties of a
phase analysis of: Phase Analysis of a to Discrete Unbounded Sequence of

theory

Sturm-Liouville Theory to Completeness of the Set

symmetries

of the Helmholtz equation: Symmetries of the Helmholtz

TE field

The TE Field

TE mode

see TE field

TEM field

The TEM Field

TEM mode

see TEM field

time, definition of

The Prüfer System

TM field

The TM Field

TM mode

see TM field

transfer function

Translation Invariant Systems

translation eigenfunction

Translations and Rotations in | Translations and Rotations in

translation generator

translation invariant

function space: Unit-Economy via the Two
systems: Translation Invariant Systems

translation operator

Isomorphic Hilbert Spaces | Orthonormal Wave Packets: General

transverse electric magnetic mode

see TEM field

transverse electric mode

see TE field

transverse magnetic mode

see TM field

triangle inequality

Inner Product Spaces | Metric Spaces | Metric Spaces

unit impulse response

see Green's function

unit-economy

Unit-Economy via the Two

principle of: Chirped Signals and the | Unit-Economy via the Two | Partial Differential Equations

unitary transformation between Hilbert spaces

vibrating cable

Sturm-Liouville Differential Equation

vibrating string

equation: Sturm-Liouville Differential Equation
kinetic energy of: Orthogonality, Reality, and Uniqueness
normal mode for: Sturm-Liouville Differential Equation
potential energy of: Orthogonality, Reality, and Uniqueness
simple: The Homogeneous Problem
total energy of: Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness

vibrational degree of freedom

energy in each: Orthogonality, Reality, and Uniqueness

vibrations in 1 dimensions

amplitude profile of: Homogeneous Boundary Conditions

wave equation

Sturm-Liouville Differential Equation

for a cylindrical cavity: Finite Interior Boundary Value to Finite Interior Boundary Value
for an imbedded string: 3. Apply Green's Identity
Klein-Gordon: 3. Apply Green's Identity
spherically symmetric solutions to: Spherically Symmetric Solutions to Spherically Symmetric Solutions
for spherically symmetric systems: Wave Equation for Spherically to Wave Equation for Spherically
static solutions to: Static Solutions to Static Multipole Field

wavelet

analysis: Wavelet Analysis to Wavelet Analysis
generation theorem: Wavelet Analysis

wavelet representation

Orthonormal Wavelet Representation

construction and properties: Construction and Properties

wavepacket representation theorem

Phase Space Representation

Wheeler's motto

Wheeler, John A.

Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness

Whittaker-Shannon sampling theorem

finite interval version: Whittaker-Shannon Sampling Theorem: The
infinite interval version: Whittaker-Shannon Sampling Theorem: The

Wiener-Khintchine formula

The Fourier Transform as

Wronskian

Wronskian determinant