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Journal of Fourier Analysis and Applications

, Volume 20, Issue 4, pp 679–714 | Cite as

Hagedorn Wavepackets in Time-Frequency and Phase Space

  • Caroline Lasser
  • Stephanie Troppmann
Article

Abstract

The Hermite functions are an orthonormalbasis of the space of square integrable functions with favourable approximation properties. Allowing for a flexible localization in position and momentum, the Hagedorn wavepackets generalize the Hermite functions also to several dimensions. Using Hagedorn’s raising and lowering operators, we derive explicit formulas and recurrence relations for the Wigner and FBI transform of the wavepackets and show their relation to the Laguerre polyomials.

Keywords

Hermite functions Hagedorn wavepackets Wigner transform  FBI transform Husismi transform Ladder operators 

Mathematics Subject Classification

42C05 42A38 65R10 

Notes

Acknowledgments

This research was supported by the German Research Foundation (DFG), Collaborative Research Center SFB-TR 109. We thank the anonymous referees for pointing us to the generalized coherent states. We also thank Matthias Nützel and Ilja Klebanov for their careful reading of the manuscript.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenMunichGermany

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