Frames for model spaces

TL;DR

This paper explores the properties and characterizations of frames within model spaces and RKHS, emphasizing their theoretical foundations and practical applications in dynamical sampling.

Contribution

It systematically investigates the intrinsic features of model space frames and their reproducing counterparts, providing new characterizations and practical examples.

Findings

Characterizations of model space frames

Analysis of reproducing counterparts

Validation through practical examples

Abstract

The concept of frames, initially introduced by Duffin and Schaeffer, gained substantial recognition decades later when Daubechies, Grossman, and Meyer highlighted its significance. Since then, frame theory has become a fundamental and widely applicable tool across diverse branches of Mathematics, Physics, and Engineering Sciences. Driven by the extensive applications of model space frames in dynamical sampling, the study delves into an exploration of frames and their properties within the model space and RKHS. Moreover, the study systematically investigates the intrinsic features of model space frames and its reproducing counterparts, thoroughly examining and analyzing various characterizations of the same. Furthermore, several examples are provided to validate the results, demonstrating the practical applicability and correctness of the theoretical findings.