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Decay of the fourier transform : analytic and geometric aspects / Alex Iosevich and Elijah Liflyand.

By: Contributor(s): Material type: TextTextPublication details: New York : Springer, 2014.Description: xii, 222 p. : illustrations ; 24 cmISBN:
  • 9783034806244 (hard cover : alk. paper)
Subject(s): DDC classification:
  • 515.2433  23 Io64
Contents:
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.
Summary: 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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Holdings
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
Total holds: 0

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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