Work

Inner and characteristic functions in polydiscs

Year: 2025

Type: preprint

Abstract: Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2502.00727

Authors: Debnath, Ramlal, Pradhan, Deepak K., Sarkar, Jaydeb

Institution: Indian Statistical Institute

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Science and Engineering Research Board

OpenAlex ID: W4407123988

Cites:

Cited by:

Related to: 10