Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 225-246 |
| Seitenumfang | 22 |
| Fachzeitschrift | Journal fur die Reine und Angewandte Mathematik |
| Jahrgang | 2015 |
| Ausgabenummer | 703 |
| Publikationsstatus | Veröffentlicht - 1 Juni 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal fur die Reine und Angewandte Mathematik, Jahrgang 2015, Nr. 703, 01.06.2015, S. 225-246.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation
AU - Bauer, Wolfram
AU - Coburn, Lewis A.
N1 - Publisher Copyright: © 2015 by De Gruyter. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84930971310&partnerID=8YFLogxK
U2 - 10.1515/crelle-2015-0016
DO - 10.1515/crelle-2015-0016
M3 - Article
AN - SCOPUS:84930971310
VL - 2015
SP - 225
EP - 246
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 703
ER -