Riesz distributions and Laplace transform in the Dunkl setting of type A
| Autor: | Margit Rösler |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Primary 33C52
Secondary 43A85 33C80 44A10 Pure mathematics Kernel (set theory) Laplace transform 010102 general mathematics Mathematics::Classical Analysis and ODEs Multiplicity (mathematics) Type (model theory) Characterization (mathematics) 01 natural sciences Measure (mathematics) Distribution (mathematics) Mathematics - Classical Analysis and ODEs Mathematics::Quantum Algebra 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Exponent 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Analysis Mathematics - Representation Theory Mathematics |
| Popis: | We study Riesz distributions in the framework of rational Dunkl theory associated with root systems of type A. As an important tool, we employ a Laplace transform involving the associated Dunkl kernel, which essentially goes back to Macdonald, but was so far only established at a formal level. We give a rigorous treatment of this transform based on suitable estimates of the type A Dunkl kernel. Our main result is a precise analogue in the Dunkl setting of a well-known result by Gindikin, stating that a Riesz distribution on a symmetric cone is a positive measure if and only if its exponent is contained in the Wallach set. For Riesz distributions in the Dunkl setting, we obtain an analogous characterization in terms of a generalized Wallach set which depends on the multiplicity parameter on the root system. Revised version; some notations changed and Theorem 5.11 improved |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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