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About 732 papers for “Bergman kernel”

Bergman Kernel and Bergman Metric

Adam Korányi · Birkhäuser Boston eBooks · 2000

In this chapter we consider general domains in ℂ n . The material discussed is easily available in the literature. Still we give here essentially complete proofs, since we can do it in very concisely and since the results will be used later in several instances.

Cited by 0

The Bergman kernel

Richard Beals, Roderick Wong · Graduate texts in mathematics · 2023

Cited by 0

The Bergman Kernel

M. Stoll · Cambridge University Press eBooks · 2009

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Cited by 1

The Bergman kernel

Gábor Székelyhidi · Graduate studies in mathematics · 2014

Cited by 0Open access

Bergman kernel and pluripotential theory

Zbigniew Błocki · Contemporary mathematics - American Mathematical Society · 2015

We survey recent applications of pluripotential theory for the Bergman kernel and metric.

Cited by 12

On the octonionic Bergman kernel

Jinxun Wang, Xingmin Li · arXiv (Cornell University) · 2016

By introducing a suitable new definition for the inner product on the octonionic Bergman space, we determine the explicit form of the octonionic Bergman kernel, in the framework of octonionic analysis which is non-commutative and non-associative.

Cited by 0Open access

Applications of Bergman kernel functions

S. Bock, M. I. Falcão, K. Guerlebeck · RepositóriUM (Universidade do Minho) · 2003

In this paper we revisit the so-called Bergman kernel method (BKM) for solving confor-mal mapping problems. This method is based on the reproducing property of the Bergman kernel function. The construction of reproducing kernel functions is not restricted to real dimension 2. Results concerning the construction of Bergman kernel functions in closed form for special domains in the framework of hypercomplex function theory suggest that BKM can also be extended to mapping problems in higher dimensions. We describe a 3-dimensional BKM-approach and present two numerical examples. 1

Cited by 0Open access

Bergman Kernel and its Transformations

Gargi Ghosh · 2015

The Bergman kernel is a very important object to study in many different areas of mathematics, namely, complex analysis, partial differential equations, differential geometry and operator theory to mention a few. Bergman kernel is an important tool for studying biholomorphic (conformal) mappings and their boundary behaviour. We discuss Hilbert spaces of complex-valued functions defined on some X such that the point evaluations are continuous for each point of X. The Bergman kernel transforms nicely under biholomorphic mappings. We discuss this transformation property in detail and include two proofs of the transformation rule using the Hilbert space structure of the Bergman space. The relationship between the Bergman kernel function of a simply connected domain and the Riemann mapping function of the domain is also mentioned. The relation between the Bergman projection and the Bergman kernel is also discussed.

Cited by 0