Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation
-
Wolfram Bauer
and
Lewis A. Coburn
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 on 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.
Funding source: DFG (Deutsche Forschungsgemeinschaft)
Award Identifier / Grant number: Emmy-Noether scholarship
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The circle method and non-lacunarity of meromorphic modular forms
- Lower bounds on Ricci flow invariant curvatures and geometric applications
- Regularized theta liftings and periods of modular functions
- The collapsing rate of the Kähler–Ricci flow with regular infinite time singularity
- Selberg zeta functions on odd-dimensional hyperbolic manifolds of finite volume
- Direct embeddings of relatively hyperbolic groups with optimal ℓp compression exponent
- Perelman's entropy functional at Type I singularities of the Ricci flow
- Classification of symmetric pairs with discretely decomposable restrictions of (𝔤,K)-modules
- Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation
Articles in the same Issue
- Frontmatter
- The circle method and non-lacunarity of meromorphic modular forms
- Lower bounds on Ricci flow invariant curvatures and geometric applications
- Regularized theta liftings and periods of modular functions
- The collapsing rate of the Kähler–Ricci flow with regular infinite time singularity
- Selberg zeta functions on odd-dimensional hyperbolic manifolds of finite volume
- Direct embeddings of relatively hyperbolic groups with optimal ℓp compression exponent
- Perelman's entropy functional at Type I singularities of the Ricci flow
- Classification of symmetric pairs with discretely decomposable restrictions of (𝔤,K)-modules
- Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation
