The Use of Frames in Sampling Theory

Beschreibung

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.

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.

Autor*in

Antonio García García

Themen in »The Use of Frames in Sampling Theory«

Sampling Theory Frames in Hilbert Spaces Including Orthonormal and Riesz Bases Harmonic Analysis Reproducing Kernel Hilbert Spaces Shift-Invariant Spaces Unitary Representation of a Group Time-Frequency Analysis

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“Each chapter closes with a list of references that includes significant results of the author and his coworkers. The book is written in a clear and organized manner, can be used by students and researchers interested in sampling theory, and fully deserves the author’s motto: For those who enjoy maths.” (Liviu Goraş, zbMATH 1572.42001, 2026)

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