The Plancherel formula says that the L 2 norm of the function is equal to the L 2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L 2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L 2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

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Produktbeschreibung

The Plancherel formula says that the L² norm of the function is equal to the L² norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L² function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L² setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

Produktdetails
Verlag: Springer Basel
Seitenzahl: 222
Erscheinungstermin: 1. Oktober 2014
Englisch
ISBN-13: 9783034806251
Artikelnr.: 44122512

Produktdetails

Verlag: Springer Basel
Seitenzahl: 222
Erscheinungstermin: 1. Oktober 2014
Englisch
ISBN-13: 9783034806251
Artikelnr.: 44122512

Herstellerkennzeichnung

Inhaltsangabe

Foreword.- Introduction.- Chapter 1. Basic properties of the Fourier transform.- Chapter 2. Oscillatory integrals and Fourier transforms in one variable.- Chapter 3. The Fourier transform of an oscillating function.- Chapter 4. The Fourier transform of a radial function.- Chapter 5. Multivariate extensions.- Appendix.- Bibliography.

Inhaltsangabe

Rezensionen

"The overall presentation is clear and the reader is carefully guided through this territory which is marked by a beautiful blend of ideas and techniques from analysis, geometry and also number theory." (Wien R. Steinbauer, Monatshefte für Mathematik, Vol. 185, 2018)

"It is an introduction to current topics in Fourier analysis, to be read and appreciated by mathematicians ... . the book is carefully designed and well written. It does a very good job of familiarizing the reader with the relevant techniques and results, relying on a beautiful interplay of analysis, geometry and number theory." (Hartmut Führ, Mathematical Reviews, January, 2016)

Decay of the Fourier Transform (eBook, PDF)

Analytic and Geometric Aspects

Decay of the Fourier Transform (eBook, PDF)

Analytic and Geometric Aspects

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