Regular generalized sampling in T-invariant subspaces of a Hilbert space

TL;DR

This paper develops a generalized sampling theory for T-invariant subspaces in Hilbert spaces, extending classical sampling methods to more structured and abstract settings involving bounded invertible operators.

Contribution

It introduces a regular generalized sampling framework in T-invariant subspaces, broadening the applicability of sampling theory beyond traditional contexts.

Findings

Established a generalized sampling theory in T-invariant subspaces

Extended classical sampling to structured Hilbert space settings

Analyzed key cases generalizing usual sampling scenarios

Abstract

A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases which generalize the usual sampling settings.