Asymptotically Orthonormal Basis and Toeplitz operators

TL;DR

This paper extends criteria for basicity of complex exponential sequences to model spaces linked with meromorphic inner functions, providing new insights into asymptotically orthonormal bases and Toeplitz operators.

Contribution

It generalizes Mitkovski's results to broader model spaces and introduces an analogue for asymptotically orthonormal bases.

Findings

Extended Toeplitz operator criteria to model spaces

Established analogue for asymptotically orthonormal basis

Connected invertibility properties to basis properties in new settings

Abstract

Recently, M. Mitkovski gave a criterion for the basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator, in the spirit of the celebrated work of Khrushchev-Nikolski-Pavlov. In our paper, we extend the results of Mitkovski to model spaces associated with meromorphic inner functions and we also give an analogue for the property of being an asymptotically orthonormal basis.