Lattice Point Identities and Shannon-Type Sampling

List of contents

Preface. About the Authors. Acknowledgment. 1.From Lattice Point to Shannon-Type Sampling Identities. 2.Obligations, Ingredients, Achievements, and Innovations. 3.Layout. 4.Euler/Poisson-Type Summation Formulas and Shannon-Type Sampling. 5.Preparatory Tools of Vector Analysis. 6.Preparatory Tools of the Theory of Special Functions. 7.Preparatory Tools of Lattice Point Theory. 8.Preparatory Tools of Fourier Analysis. 9.Euler–Green Function and Euler-Type Summation Formula. 10.Hardy–Landau-Type Lattice Point Identities (Constant Weight). 11.Hardy–Landau-Type Lattice Point Identities (General Weights). 12.Bandlimited Shannon-Type Sampling (Preparatory Results). 13.Lattice Ball Shannon-Type Sampling. 14.Gauss-Weierstrass Mean Euler-Type Summation Formulas and Shannon-Type Sampling. 15.From Gauss-Weierstrass to Ordinary Lattice Point Poisson–Type Summation. 16.Shannon-Type Sampling Based on Poisson-Type Summation Formulas. 17.Paley–Wiener Space Framework and Spline Approximation. 18.Poisson-Type Summation Formulas over Euclidean Spaces. 19.Shannon–Type Sampling Based on Poisson–Type Summation Formulas over Euclidean Spaces. 20.Trends, Progress, and Perspectives. Bibliography. Index.

About the author

Willi Freeden, M. Zuhair Nashed

Summary

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.

Product details

• Authors: Willi Freeden, Willi (Technical University of Kaiserslau Freeden, Willi Nashed Freeden, Freeden Willi, M. Zuhair Nashed
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 31.12.2019
• EAN: 9780367375638
• ISBN: 978-0-367-37563-8
• No. of pages: 305
• Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, TECHNOLOGY & ENGINEERING / Telecommunications, MATHEMATICS / Algebra / General, Communications engineering / telecommunications