Brennecken, Dominik: Contributions to Dunkl theory : Dominik Brennecken ; Betreuung durch Prof. Dr. Margit Rösler. Paderborn, 2024
Inhalt
- Introduction
- I General results in Dunkl theory
- Introduction to Dunkl theory
- Root systems and their reflection groups
- Introduction to rational Dunkl theory
- Riemannian symmetric spaces of Euclidean type
- Dunkl convolution and elliptic regularity
- Dunkl convolution
- (Singular-)support of Dunkl convolutions
- Hypoellipticity of elliptic Dunkl operators
- Elliptic regularity of Dunkl operators
- Multitemporal wave equation
- Results in trigonometric Dunkl theory
- II Dunkl theory in line with radial analysis on symmetric cones
- Radial analysis on symmetric cones
- Laplace transform of hypergeometric functions
- Introduction
- The type A Dunkl setting
- Jack polynomials and Macdonald's conjecture
- Laplace transform of the Cherednik kernel
- Macdonald's hypergeometric series
- Convolution of type A Riesz distributions
- The binomial formula for the Cherednik kernel
- A Post-Widder inversion formula
- Bessel functions, Hankel transform, Zeta integrals
- III Limit transitions and Olshanski pairs
- IV Appendix