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Further properties of the Bergman spaces of slice regular functions
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Fabrizio Colombo
Veröffentlicht/Copyright:
6. Oktober 2015
Abstract
We continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.
Keywords: Slice regular functions; Bergman kernel; Bergman-Fueter transform; Schwarz reflection principle
Received: 2013-11-26
Published Online: 2015-10-6
Published in Print: 2015-10-1
© 2015 by Walter de Gruyter Berlin/Boston
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Artikel in diesem Heft
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
Schlagwörter für diesen Artikel
Slice regular functions;
Bergman kernel;
Bergman-Fueter transform;
Schwarz reflection principle
Artikel in diesem Heft
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
