Representing systems of reproducing kernels in spaces of analytic functions

TL;DR

This paper constructs representing systems of reproducing kernels in Hardy spaces and weighted Hardy spaces, providing an elementary approach to understanding their structure and properties.

Contribution

It introduces an elementary construction method for representing systems of Cauchy and reproducing kernels in Hardy and weighted Hardy spaces.

Findings

Constructed representing systems in Hardy spaces

Extended constructions to weighted Hardy spaces

Provided elementary approach for kernel representations

Abstract

We give an elementary construction of representing systems of the Cauchy kernels in the Hardy spaces $H^p$, $1 \le p <\infty$, as well as of representing systems of reproducing kernels in weighted Hardy spaces.