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001			CR9781316227619
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007			cr||||||||||||
008			141020s2015||||enk o ||1 0|eng|d
020			_a9781316227619 (ebook)
020			_z9781107107359 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA403.5 _b.M38 2015
082	0	4	_a515.2/433 _223
100	1		_aMattila, Pertti, _eauthor.
245	1	0	_aFourier analysis and Hausdorff dimension / _cPertti Mattila.
246	3		_aFourier Analysis & Hausdorff Dimension
264		1	_aCambridge : _bCambridge University Press, _c2015.
300			_a1 online resource (xiv, 440 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge studies in advanced mathematics ; _v150
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aPreface -- Acknowledgements -- Introduction -- Part 1. Preliminaries and some simpler applications of the Fourier transform. Measure theoretic preliminaries -- Fourier transforms -- Hausdorff dimension of projections and distance sets -- Exceptional projections and Sobolev dimension -- Slices of measures and intersections with planes -- Intersections of general sets and measures -- Part 2. Specific constructions. Cantor measures -- Bernoulli convolutions -- Projections of the four-corner Cantor set -- Besicovitch sets -- Brownian motion -- Riesz products -- Oscillatory integrals (stationary phase) and surface measures -- Part 3. Deeper applications of the Fourier transform. Spherical averages and distance sets -- Proof of the Wolff-Erdoğan Theorem -- Sobolev spaces, Schrödinger equation and spherical averages -- Generalized projections of Peres and Schlag -- Part 4. Fourier restriction and Kakeya type problems. Restriction problems -- Stationary phase and restriction -- Fourier multipliers -- Kakeya problems -- Dimension of Besicovitch sets and Kakeya maximal inequalities -- (n, k) Besicovitch sets -- Bilinear restriction.
520			_aDuring the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.
650		0	_aFourier transformations.
650		0	_aMeasure theory.
650		0	_aMathematical analysis. _960397
776	0	8	_iPrint version: _z9781107107359
830		0	_aCambridge studies in advanced mathematics ; _v150.
856	4	0	_uhttps://doi.org/10.1017/CBO9781316227619
907			_a.b16846011 _b2020-12-22 _c2020-12-22
942			_n0
998			_a1 _b2020-12-22 _cm _da _feng _genk _y0 _z.b16846011
999			_c651944 _d651944