The Hilbert-Schmidt analyticity associated with infinite-dimensional unitary groups

TL;DR

This paper explores Hilbert-Schmidt analytic extensions in Hardy spaces over infinite-dimensional unitary groups, focusing on basis functions, kernels, and boundary behaviors.

Contribution

It introduces new methods for analyzing Hilbert-Schmidt analyticity in infinite-dimensional settings, including basis construction and kernel formulas.

Findings

Established orthogonal bases for Hilbert-Schmidt polynomials

Derived integral formulas and reproducing kernels

Analyzed boundary value problems in Hardy spaces

Abstract

The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt polynomials, reproducing kernels, integral formulas and boundary values are investigated.