Decay of the fourier transform : analytic and geometric aspects / Alex Iosevich and Elijah Liflyand.
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TextPublication details: New York : Springer, 2014.Description: xii, 222 p. : illustrations ; 24 cmISBN: - 9783034806244 (hard cover : alk. paper)
- 515.2433 23 Io64
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.2433 Io64 (Browse shelf(Opens below)) | Available | 136219 |
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| 515.2433 In61 Wavelet analysis and its applications ( WAA ) | 515.2433 In61(92) Fourier analysis and partial differential equations : proceedings | 515.2433 Io64 Fourier analysis and partial differential equations | 515.2433 Io64 Decay of the fourier transform : | 515.2433 J12 Fourier series and orthogonal polynomials | 515.2433 J12 Fourier series and orthogonal polynomials | 515.2433 J25 Wavelet analysis on local fields of positive characteristic / |
Includes bibliographical references and index.
1. Basic properties of the Fourier transform --
2. Oscillatory integrals --
3. The Fourier transform of convex and oscillating functions --
4. The Fourier transform of a radial function --
5. L²-average decay of the Fourier transform of a characteristic function of a convex set --
6. L¹-average decay of the Fourier transform of a characteristic function of a convex set --
7. Geometry of the Gauss map and lattice points in convex domains --
8. Average decay estimates for Fourier transforms of measures supported on curves--
Epilogue--
Bibliography--
Index.
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.
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