Weyl transform and Weyl multipliers associated with locally compact abelian groups
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In this paper, we extend to the context of locally compact abelian groups, the notion of Weyl transform. We also define and characterize Weyl multipliers for certain function spaces. A dual space characterization is provided for the space of Weyl multipliers on \(L^p\) spaces. Finally we also study the twisted shift-invariant subspaces.
KeywordsLocally compact abelian group Weyl transform Twisted convolution Twisted Figà-Talamanca Herz algebra Twisted shift-invariant spaces
Mathematics Subject ClassificationPrimary 43A15 43A25 Secondary 22B05 43A32
The authors would like to thank the unknown referee for meticulously reading the paper and giving us some valuable suggestions. The proof of Proposition 2.8 (c) was suggested by Prof. Rajaram Bhat through a personal communication. We thank Prof. Rajaram Bhat (Indian Statistical Institute, Bangalore) for his kind response to our query.
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