On a Construction of L. Hua for Positive Reproducing Kernels
Steven G. Krantz
TL;DR
This paper explores a positive reproducing kernel for holomorphic functions on complex domains, utilizing L. Hua's method, with applications and connections to Berezin's quantization of Kähler manifolds.
Contribution
It introduces a new construction of positive reproducing kernels inspired by L. Hua's ideas, extending their application to complex analysis and geometric quantization.
Findings
Developed a new positive reproducing kernel for holomorphic functions.
Connected Hua's construction to Berezin's quantization of Kähler manifolds.
Provided applications demonstrating the kernel's utility.
Abstract
We study a positive reproducing kernel for holomorphic functions on a domain in a complex space. The technique is based on an idea of L. Hua. Applications are provided. These ideas were developed in another context (quantization of K\"{a}hler manifolds) by Berezin.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Matrix Theory and Algorithms · Holomorphic and Operator Theory