Mathematics > Functional Analysis
[Submitted on 18 Jul 2014]
Title:On the chaotic behavior of the Dunkl heat semigroup on weighted $ L^p $ spaces
View PDFAbstract:In this paper we study the chaotic behaviour of the heat semigroup generated by the Dunkl-Laplacian on weighted $ L^p$ spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces $ L^p(\R^n, (\varphi_{i\rho}(x))^2 dx) $ where $ \varphi_{i\rho} $ is the Euclidean spherical function. The behaviour is very similar to the case of the Laplace-Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar.
Submission history
From: Sundaram Thangavelu [view email][v1] Fri, 18 Jul 2014 14:31:20 UTC (26 KB)
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