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

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dc.identifier.uri http://dx.doi.org/10.15488/3128
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/3158
dc.contributor.author Bauer, Wolfram
dc.contributor.author Coburn, Lewis A.
dc.date.accessioned 2018-04-18T13:04:38Z
dc.date.available 2018-04-18T13:04:38Z
dc.date.issued 2015
dc.identifier.citation Bauer, W.; Coburn, L.A.: Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation. In: Journal fur die Reine und Angewandte Mathematik 2015 (2015), Nr. 703, S. 225-246. DOI: https://doi.org/10.1515/crelle-2015-0016
dc.description.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. © 2015 by De Gruyter. eng
dc.language.iso eng
dc.publisher Berlin : De Gruyter
dc.relation.ispartofseries Journal fur die Reine und Angewandte Mathematik 2015 (2015), Nr. 703
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject Heat flow eng
dc.subject Bergman spaces eng
dc.subject Lipschitz constants eng
dc.subject.ddc 510 | Mathematik ger
dc.title Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation
dc.type article
dc.type Text
dc.relation.issn 0075-4102
dc.relation.doi https://doi.org/10.1515/crelle-2015-0016
dc.bibliographicCitation.issue 703
dc.bibliographicCitation.volume 2015
dc.bibliographicCitation.firstPage 225
dc.bibliographicCitation.lastPage 246
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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