Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem

TL;DR

This paper develops a new function theory framework for the tetrablock, establishing realization, interpolation, extension, and Toeplitz corona theorems, advancing the understanding of operator theory in this domain.

Contribution

It introduces a Schur-Agler class for the tetrablock and proves key theorems analogous to classical results, expanding the theoretical foundation.

Findings

Established a realization theorem for the Schur-Agler class on the tetrablock.

Proved an interpolation theorem specific to the tetrablock setting.

Extended the Toeplitz corona theorem to the tetrablock context.

Abstract

We introduce a Schur-Agler type class associated with the tetrablock and establish a realization theorem for this class. Furthermore, we provide a tetrablock analog of the interpolation theorem, extension theorem, and the Toeplitz corona theorem.