Chaotic behavior of the Riesz transforms for Hermite expansions |
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| Authors: | Teresa Bermú dez,Antonio Bonilla,Jose L. Torrea |
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| Affiliation: | a Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
b Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28049 Madrid, Spain |
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| Abstract: | We prove a characterization for hypercyclic and chaotic unbounded unilateral weighted shifts of order p. As applications we obtain that the natural derivatives associated to Hermite expansions are chaotic. On the other hand, the corresponding Riesz transforms are not hypercyclic and even more they are a kind of border line operator which separates the chaotic behavior. |
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| Keywords: | Chaotic Hypercyclic Unbounded weighted shift Hermite and Laguerre expansions Heat diffusion semigroup Riesz transform |
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