000			03047pam a2200313 a 4500
001			00044508
003			DLC
005			20231011101759.0
008			000608s2001 mau 001 0 eng
010			_a00044508
020			_a9780817640224
020			_a0817640223
040			_aDLC _cDLC _dDLC _dOrLoB-B
050	0	0	_aTK5102.9 _b.G76 2001
082			_a621.382 _bGRO
090			_aTK5102.9 _bGro
100	1		_aGröchenig, Karlheinz.
245	1	0	_aFoundation of time-frequency analysis : _bwith 15 figures / _cKarlheinz Gröchenig.
260			_aBoston : _bBirkhäuser, _cc2001.
300			_axv, 359 p. : _bill. ; _c25 cm.
440		0	_aApplied and numerical harmonic analysis.
504			_aIncludes bibliographical references (p. 335-353) and index.
505			_aItinerary Karlheinz Gröchenig Pages 1-2 Basic Fourier Analysis Karlheinz Gröchenig Pages 3-20 Time-Frequency Analysis and the Uncertainty Principle Karlheinz Gröchenig Pages 21-36 The Short-Time Fourier Transform Karlheinz Gröchenig Pages 37-58 Quadratic Time-Frequency Representations Karlheinz Gröchenig Pages 59-82 Discrete Time-Frequency Representations: Gabor Frames Karlheinz Gröchenig Pages 83-101 Existence of Gabor Frames Karlheinz Gröchenig Pages 103-126 The Structure of Gabor Systems Karlheinz Gröchenig Pages 127-146 Zak Transform Methods Karlheinz Gröchenig Pages 147-174 The Heisenberg Group: A Different Point of View Karlheinz Gröchenig Pages 175-201 Wavelet Transforms Karlheinz Gröchenig Pages 203-214 Modulation Spaces Karlheinz Gröchenig Pages 215-244 Gabor Analysis of Modulation Spaces Karlheinz Gröchenig Pages 245-275 Window Design and Wiener’s Lemma Karlheinz Gröchenig Pages 277-299 Pseudodifferential Operators Karlheinz Gröchenig Pages 301-327 Back Matter Pages 329-360
520	1		_a"Time-frequency analysis is a source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued mainly in engineering, but recently - with the development of wavelet theory - it has emerged as a thriving field of applied mathematics." "This book presents the first systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honoring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e., the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements."--BOOK JACKET.
650		0	_aSignal processing _xMathematics.
650		0	_aTime-series analysis.
650		0	_aFrequency spectra.
942			_2ddc _cPROJECT
999			_c39878 _d39878