Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation

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Authors

  • Wolfram Bauer
  • Lewis A. Coburn

Research Organisations

External Research Organisations

  • University at Buffalo (UB)
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Details

Original languageEnglish
Pages (from-to)225-246
Number of pages22
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
Issue number703
Publication statusPublished - 1 Jun 2015

Abstract

We show that, for f any uniformly continuous (UC) complex-valued function on real Euclidean n-space ℝn, the heat flow f˜(t) is Lipschitz for all t > 0 and f˜(t) converges uniformly to f as t → 0. Analogously, let Ω be any irreducible bounded symmetric (Cartan) domain in complex n-space ℂn and consider the Bergman metric β(·,·) on Ω. For f any β-uniformly continuous function Ω, we show that there is a Berezin-Harish-Chandra flow of real analytic functions Bλf which is β-Lipschitz for each λ ≥ p (p, the genus of Ω) and Bλf converges uniformly to f as λ → ∞. For a certain subspace of UC we obtain stronger approximation results and we study the asymptotic behaviour of the Lipschitz constants.

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Cite this

Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation. / Bauer, Wolfram; Coburn, Lewis A.
In: Journal fur die Reine und Angewandte Mathematik, Vol. 2015, No. 703, 01.06.2015, p. 225-246.

Research output: Contribution to journal › Article › Research › peer review

Bauer W, Coburn LA. Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation. Journal fur die Reine und Angewandte Mathematik. 2015 Jun 1;2015(703):225-246. doi: 10.1515/crelle-2015-0016
Bauer, Wolfram ; Coburn, Lewis A. / Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation. In: Journal fur die Reine und Angewandte Mathematik. 2015 ; Vol. 2015, No. 703. pp. 225-246.
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