TITLE: Wavelet Methods in  Harmonic Analysis, Nonlinear Approximation and Probability.

Prof. Gerard Kerkyacharian

PERIOD: March-April 2009

TIME: To be defined

PROGRAM:

1) Background in Fourier Analysis. Schauder Basis, Frame and Riesz Basis.

2) Sobolev and Besov spaces. Linear and Nonlinear Approximation. Interpolation Theory.

3) Wavelet constructions. Characterization of function spaces by wavelet expansions, Besov and Triebel-Lizorkin spaces.

4) Generalization of localized tight frames:  Construction of needlets on the sphere through Spherical Harmonics, and needlets
on the interval through Jacobi Polynomials.

5) Applications to Probability and Mathematical Statistics: Brownian Motion, density estimation, regression and inverse problems. Wavelet analysis for isotropic random fields. Application to Radon transform and tomography .

For further information please contact Prof. D. Marinucci: marinucc "at" mat.uniroma2.it