Agnieszka Hejna (University of Wroclaw) |
Titel: Harmonic analysis in the rational Dunkl setting
Abstract:
Dunkl theory is a generalization of Fourier analysis and special function
theory related to root systems and reflections groups. The Dunkl operators T_j, which were introduced by C. F. Dunkl in 1989, are deformations of directional derivatives by difference operators related to the reflection group. The goal of this talk will be to study harmonic analysis and Hardy spaces in the rational Dunkl setting. The first part will be devoted to two results: improved estimates of the heat kernel h_t(x,y) of the Dunkl heat semigroup generated by the Dunkl--Laplace operator Delta_k=\sum_{j=1}^NT_j^2, and a theorem regarding the support of Dunkl translations of L^2 compactly supported functions (not necessarily radial). This kind of results turn out to be useful tools in studying harmonic analysis in Dunkl setting. We will discuss this kind of applications in the second part of the talk. We will discuss how our tools can be used to for studying singular integrals of convolution type or Littlewood-Paley square functions in the Dunkl setting.
This talk is based on the joint articles with J-Ph. Anker and J. Dziubanski.
Bei Interesse an einer Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich oder Benjamin Küster Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.