Revista Matemática Iberoamericana

Heat kernel transform for nilmanifolds associated to the Heisenberg group

Bernhard Krötz , Sundaram Thangavelu , and Yuan Xu

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Abstract

We study the heat kernel transform on a nilmanifold $M$ of the Heisenberg group. We show that the image of $L^2(M)$ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.

Article information

Source
Rev. Mat. Iberoamericana, Volume 24, Number 1 (2008), 243-266.

Dates
First available in Project Euclid: 16 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1216247101

Mathematical Reviews number (MathSciNet)
MR2435972

Zentralblatt MATH identifier
1153.22009

Subjects
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 35H20: Subelliptic equations 35K05: Heat equation 58J35: Heat and other parabolic equation methods

Keywords
Heisenberg group nilmanifolds Bergman spaces heat kernel Hermite and Laguerre functions

Citation

Krötz , Bernhard; Thangavelu , Sundaram; Xu , Yuan. Heat kernel transform for nilmanifolds associated to the Heisenberg group. Rev. Mat. Iberoamericana 24 (2008), no. 1, 243--266. https://projecteuclid.org/euclid.rmi/1216247101


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References

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