Sampling in unitary invariant subspaces associated to LCA groups

TL;DR

This paper develops a unified sampling theory for unitary invariant subspaces linked to LCA groups, leveraging frame theory and matrix analysis to handle diverse practical problems efficiently.

Contribution

It introduces a general sampling framework for LCA group-associated subspaces, unifying various existing results and simplifying notation.

Findings

Unified sampling results for LCA groups

Application of frame theory and matrix analysis

Simplification of complex notation

Abstract

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed.