Decay of the Fourier Transform

Analytic and Geometric Aspects

Inbunden, Engelska, 2014

1 167 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2014-10-10
Mått:155 x 235 x 19 mm
Vikt:524 g
Format:Inbunden
Språk:Engelska
Antal sidor:222
Upplaga:2014
Förlag:Springer Basel
ISBN:9783034806244

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"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 Fuhr, Mathematical Reviews, January, 2016)

Innehållsförteckning

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.