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Analyticity of the Schrödinger propagator on the Heisenberg group

Monatshefte für Mathematik volume 168, pages 279–303 (2012)Cite this article

Abstract

We discuss the analytic extension property of the Schrödinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.

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Authors and Affiliations

  1. School of Mathematics, National Institute of Science Education and Research, IOP Campus, Bhubaneswar, 751005, India

    S. Parui

  2. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    P. K. Ratnakumar

  3. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    S. Thangavelu

Authors
  1. S. Parui
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  2. P. K. Ratnakumar
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  3. S. Thangavelu
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Corresponding author

Correspondence to S. Parui.

Additional information

Communicated by K. Gröchenig.

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Parui, S., Ratnakumar, P.K. & Thangavelu, S. Analyticity of the Schrödinger propagator on the Heisenberg group. Monatsh Math 168, 279–303 (2012). https://doi.org/10.1007/s00605-012-0424-7

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  • DOI: https://doi.org/10.1007/s00605-012-0424-7

Keywords

  • Schrödinger equation
  • Oscillatory group
  • Special Hermite expansion
  • Heisenberg group
  • Sublaplacian

Mathematics Subject Classification (1991)

  • Primary 22E30
  • Secondary 35G10
  • 47A63