To sign up for this working group, enroll for 3 credits in 693 (Mityagin), call number 13062-4.

Time (tentative): Mondays, 4:30 - 6:20 pm.

We will discuss interlacing questions of elementary theory of pseudo-differential operators (with special interest in spectral analysis of Schroedinger operators) and systems of orthogonal polynomials, in particular, in the context of wavelets analysis and their applications in signal processing, image coding and - depending on the participants' interest - in numerical analysis.

Sessions format: presentation of chosen questions by participants, both students and faculty; discussion of problems given every week (educational ones and research type); papers from current mathematical journals.

Prerequisites: Knowledge of advanced calculus and elementary linear algebra are important. More advanced topics (baby-real analysis, etc.) will be useful but the discussion will cover all necessary or raised questions.

Tentative literature:

• M. Reed, B. Simon, Fourier Analysis, Self-Adjointness (Vol. 2, Methods of Mordern Mathematical Physics), Academic Press.
• I. Daubechies, Ten Lectures on Wavelets, SIAM Publishers, Philadelphia, 1992.
• Journal of Approximation Theory (ed. P. Nevai and A. Ron), Elsevier Constructive Approximation Theory; Journal of Functional Analysis, etc.