000			02940nam a22003738i 4500
001			CR9780511530029
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090409s1993||||enk o ||1 0|eng|d
020			_a9780511530029 (ebook)
020			_z9780521434645 (hardback)
020			_z9780521060974 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA404 _b.S64 1993
082	0	0	_a515/.2433 _220
100	1		_aSogge, Christopher D. _q(Christopher Donald), _d1960- _eauthor.
245	1	0	_aFourier integrals in classical analysis / _cChristopher D. Sogge.
264		1	_aCambridge : _bCambridge University Press, _c1993.
300			_a1 online resource (x, 236 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v105
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_a5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n].
520			_aFourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions.
650		0	_aFourier series.
650		0	_aFourier integral operators.
776	0	8	_iPrint version: _z9780521434645
830		0	_aCambridge tracts in mathematics ; _v105.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511530029
999			_c517781 _d517779