García A.G. The Use of Frames in Sampling Theory

Springer, 2024. — 314 p.This book provides a comprehensive review of regular sampling based on frame theory in a separable Hilbert space. Thus, sampling theory has common features in almost all situations: classical theory, Kramer sampling theory, and finite sampling or sampling Hilbert–Schmidt operators. In addition, the transversality of sampling theory with other mathematical fields appears, in an easy way. The first three chapters of the book can be used as an introduction to sampling theory, while the rest of the chapters are addressed to introduce the interested reader in the research on the topic.Preface
List of Symbols
What Does Sampling Theory Mean?
Basic Sampling Theory
Sampling in Shift-Invariant Subspaces
A Review on Kramer Sampling Theorem
A Generalized Sampling Theory
Finite Frames Related to Sampling in Finite-Dimensional U-Invariant Subspaces
Sampling in Shift-Invariant-Like Subspaces of Hilbert-Schmidt Operators
Index