Probabilistic Aspect of Harmonic Analysis

Probabilistic Aspect of Harmonic Analysis

28 April, 2012 -  05 May, 2012 | Będlewo



The program covers a number of topics from analysis and probability. Both continuous and discrete settings are considered. The range, reflecting interests of 32 members of two teams (Wrocław University and Technical University of Wrocław), is by necessity, quite broad.

1. Analysis related to Lie groups and their homogeneous spaces.
- L^p spectral multipliers
- dispersive equations (Schrödinger equation, wave equation, Klein-Gordon)
in negative curvature (harmonic spaces, symmetric spaces )
-questions of harmonic analysis related to curvature
- Schrodinger operators related to various Laplacians on Euclidean spaces
- spectral analysis of Hodge-Laplacians
- special functions associated to root systems
(Dunkl, Heckman-Opdam, Cherednik-Macdonald )
-Poisson kernels on NA groups
-Hardy theory and Henkel operators
-uncertainty principle
-multiparameter singular integrals on nilpotent Lie groups
-function spaces on quasimetric measure spaces, wavelet systems
-C* algebras of Lie groups
-Fourier transform on solvable Lie groups
-actions of compact groups on nilpotent Lie groups
-weighted group algebras
-orthogonal polynomials and moment problems
-heat kernels connected with orthogonal expansions

2. Analysis and probability in various contexts
--asymptotic harmonic analysis, random matrices
-heat kernel analysis
-heat kernels and random walks in negative curvature (symmetric spaces, buildings)
-spectral distributions of discrete Laplace operators and large scale spectral geometry
-random recursions and their stationary measures
- iterated random functions, random difference equations
- Markov renewal theory
- fixed point equations related to the smoothing transform, branching processes
- random walks on groups- quantitative limit laws
- central limit theorems in connection with some problems of signal processing
- random walks in random scenery
- self interacting random processes
- potential theory of Levy Processes
- processes that are traces of reflected Brownian motion

3. Ergodic theory of group actions
- actions of endomorphisms of tori, solenoids and other compact groups
- lattice subgroups and ergodic theorems


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