Multi-valued weighted composition operators on Fock space

TL;DR

This paper investigates multivalued linear operators, called linear relations, on weighted composition transforms in Fock space, characterizing their fundamental properties through algebraic conditions involving their symbols.

Contribution

It provides a comprehensive analysis of basic properties of multivalued weighted composition operators on Fock space, including criteria for closed graph, boundedness, symmetry, and isometry.

Findings

Characterization of closed graph property

Criteria for boundedness and isometry

Conditions for symmetry in linear relations

Abstract

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols.