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Hermitian nilpotent lie groups: Harmonic analysis as spectral theory of Laplacians

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Part of the Lecture Notes in Mathematics book series (2803,volume 1494)

Abstract

In this paper, we introduce a class of nilpotent Lie groups which include Heisenberg group as a particular example, and study harmonic analysis on these groups as spectral theory of the associated sub-Laplacians instead of the representation theory.

Keywords

  • Plan Wave
  • Harmonic Analysis
  • Fourier Series
  • Measurable Function
  • Normed Space

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Reference

  1. R. S. Strichartz, Harmonic analysis as spectral theory of Laplacian, to appear in J. Func. Anal.

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  2. L. Hörmander, Hypoelliptic second-order differntial equations, Acta. Math. 119 (1967), 147–171.

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  3. R. D. Ogdean, S. Vági, Harmonic analysis of a nilpotent group and function theory on Siegel domain of type II, Adv. in Math., 33 (1979), 31–92.

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© 1991 Springer-Verlag

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Sun, Lm. (1991). Hermitian nilpotent lie groups: Harmonic analysis as spectral theory of Laplacians. In: Cheng, MT., Deng, DG., Zhou, XW. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087770

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  • DOI: https://doi.org/10.1007/BFb0087770

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54901-7

  • Online ISBN: 978-3-540-46474-7

  • eBook Packages: Springer Book Archive