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Hermite Multipliers on Modulation Spaces

  • Divyang G. Bhimani
  • Rakesh Balhara
  • Sundaram ThangaveluEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)

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.

Keywords

Hermite multipliers Modulation spaces Wave and Schrödinger equations 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Divyang G. Bhimani
    • 1
  • Rakesh Balhara
    • 2
  • Sundaram Thangavelu
    • 2
    Email author
  1. 1.TIFR Centre for Applicable MathematicsBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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