Decay of the Fourier transform analytic and geometric aspects
1. Basic properties of the Fourier transform2. 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...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Basel, Heidelberg u.a.
Birkhäuser u.a.
2014
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| Schlagworte: | |
| Online Zugang: | Verlagsangaben Inhaltsverzeichnis Cover Inhaltstext Inhaltstext |
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| Zusammenfassung: | 1. Basic properties of the Fourier transform2. 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. 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-- 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-- |
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| Beschreibung: | Literaturverz. S. 207 - 219 |
| Beschreibung: | XII, 222 S. graph. Darst. |
| ISBN: | 9783034806244 978-3-0348-0624-4 3034806248 3-0348-0624-8 |