J-contractive operator valued functions, vector valued de Branges spaces and functional models

TL;DR

This paper investigates vector valued de Branges spaces derived from J-contractive operator valued functions and examines their application in modeling symmetric operators with infinite deficiency indices.

Contribution

It introduces a framework connecting J-contractive functions with vector valued de Branges spaces and their use in functional models for symmetric operators.

Findings

Established a link between J-contractive functions and de Branges spaces.

Developed a functional model for symmetric operators with infinite deficiency indices.

Enhanced understanding of operator theory through these new space constructions.

Abstract

The aim of this paper is to study the vector valued de Branges spaces, which are based on $J$-contractive operator valued analytic functions, and to explore their role in the functional models for simple, closed, densely defined, symmetric operators with infinite deficiency indices.