Unbounded Weyl transform on the Euclidean motion group and Heisenberg motion group

2021/06/24 by Somnath Ghosh, Ghosh, Somnath, R. K. Srivastava +1
Mathematics · #33C10 #43A30 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 43A15 #Secondary 33C05

paper · pdf · doi:10.48550/arxiv.2106.15704

openalex publication_date 2021/06/24 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28

Abstract

In this article, we define Weyl transform on second countable type - I locally compact group G, and as an operator on L²(G), we prove that the Weyl transform is compact when the symbol lies in L^p(G× G) with 1≤ p≤ 2. Further, for the Euclidean motion group and Heisenberg motion group, we prove that the Weyl transform can not be extended as a bounded operator for the symbol belongs to L^p(G× G) with 2

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