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Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of \(SL(2,\mathbb {R})\)

  • Allesandra CauliEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We consider the subgroup G of \(SL(2,\mathbb {R})\) consisting of shearing and dilations, and we study the decay at infinity of the matrix coefficients of the metaplectic representation restricted to G. We prove weak-type estimates for such coefficients, which are uniform for functions in the modulation space \(M^1\). This work represents a continuation of a project aiming at studying weak-type and Strichartz estimates for unitary representations of non-compact Lie groups.

Notes

Acknowledgements

I am very indebted to Professors Fabio Nicola and Elena Cordero for discussions and remarks which improved this paper in an essential way.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTorinoItaly

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