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Published in:
Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017) Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Hermite Multipliers on Modulation Spaces

Authors : Divyang G. Bhimani, Rakesh Balhara, Sundaram Thangavelu

Published in: Analysis and Partial Differential Equations: Perspectives from Developing Countries

Publisher: Springer International Publishing

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Abstract

We study multipliers associated to the Hermite operator \(H=-\varDelta + |x|^2\) on modulation spaces \(M^{p,q}(\mathbb R^d)\). We prove that the operator m(H) is bounded on \(M^{p,q}(\mathbb R^d)\) under standard conditions on m,  for suitable choice of p and q. As an application, we point out that the solutions to the free wave and Schrödinger equations associated to H with initial data in a modulation space will remain in the same modulation space for all times. We also point out that Riesz transforms associated to H are bounded on some modulation spaces.

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previous chapter On Nuclear -Multipliers Associated to the Harmonic Oscillator
next chapter Potential Theory Results for a Class of PDOs Admitting a Global Fundamental Solution
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Metadata
Title
Hermite Multipliers on Modulation Spaces
Authors
Divyang G. Bhimani
Rakesh Balhara
Sundaram Thangavelu
Copyright Year
2019
Book
Analysis and Partial Differential Equations: Perspectives from Developing Countries

Print ISBN: 978-3-030-05656-8

Electronic ISBN: 978-3-030-05657-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-05657-5_5

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