Computability of Frames in Computable Hilbert Spaces

TL;DR

This paper explores the computability of frames in Hilbert spaces, providing definitions, characterizations, and conditions for the existence of computable dual frames, advancing the theoretical understanding of computational aspects in signal processing frameworks.

Contribution

It introduces the concept of computable frames, offers computable characterizations, and establishes conditions for computable dual frames in Hilbert spaces, which is a novel theoretical development.

Findings

Defined computable frames in Hilbert spaces

Provided computable characterizations of frames

Established necessary and sufficient conditions for computable dual frames

Abstract

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations. Also, the notion of duality of frames in the context of computability has been studied. Finally, a necessary and sufficient condition for the existence of a computable dual frame is obtained.