Lattice Point Identities and Shannon-Type Sampling (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) - Hardcover

Freeden, Willi; Nashed, M. Zuhair

Hardcover

ISBN 10: 036737563X ISBN 13: 9780367375638

Verlag: Chapman and Hall/CRC, 2019

Inhaltsangabe

Lattice Point Identities and Shannon-Type Sampling demonstrates that significant roots of many recent facets of Shannon's sampling theorem for multivariate signals rest on basic number-theoretic results.

This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space.

All in all, the context of this book represents the fruits of cross-fertilization of various subjects, namely elliptic partial differential equations, Fourier inversion theory, constructive approximation involving Euler and Poisson summation formulas, inverse problems reflecting the multivariate antenna problem, and aspects of analytic and geometric number theory.

Features:

• New convergence criteria for alternating series in multi-dimensional analysis
• Self-contained development of lattice point identities of analytic number theory
• Innovative lattice point approach to Shannon sampling theory
• Useful for students of multivariate constructive approximation, and indeed anyone interested in the applicability of signal processing to inverse problems.

Über diesen Titel

Über die Autorin bzw. den Autor

Willi Freeden, M. Zuhair Nashed

Details zur Ausgabe

• Verlag: Chapman and Hall/CRC
• Erscheinungsdatum: 2019
• Sprache: Englisch
• ISBN 10: 036737563X
• ISBN 13: 9780367375638
• Einband: Tapa dura
• Auflage: 1
• Anzahl der Seiten: 305
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar