000			02189nam a2200289Ia 4500
003			OSt
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008			220909b |||||||| |||| 00| 0 eng d
020			_a0387988998
040			_aCSL _beng _cCSL
041			_aeng.
084			_aB36M P0 _qCSL
100			_aBachman, George _eauthor. _9821529
245		0	_aFourier and Wavelet Analysis
260			_aNew York : _b Springer-Verlag, _c2000.
300			_aix, 505p
490			_aUniversitext
500			_aIncludes Bibliographical references 489-496p; Index 497-505p
520			_aglobalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue invented his integral; the theorem mentioned above was one of the first uses he made of it (Sec. 4.18). Denjoy, with the same motivation, extended the integral even further. Concurrently, the emerging point of view that things could be decom­ posed into waves and then reconstituted infused not just mathematics but all of science. It is impossible to quantify the role that this perspective played in the development of the physics of the nineteenth and twentieth centuries, but it was certainly great. Imagine physics without it. We develop the standard features of Fourier analysis-Fourier series, Fourier transform, Fourier sine and cosine transforms. We do NOT do it in the most elegant way. Instead, we develop it for the reader who has never seen them before. We cover more recent developments such as the discrete and fast Fourier transforms and wavelets in Chapters 6 and 7. Our treatment of these topics is strictly introductory, for the novice. (Wavelets for idiots?) To do them properly, especially the applications, would take at least a whole book.
650			_aFourier analysis. _9821530
650			_aInfinite Series. _9821531
650			_aMathematics _9821532
700			_a Beckenstein, Edward _eco-author. _9821533
700			_aNarici, Lawrence _eco-author. _9821534
942			_hB36M P0 _cTEXL _2CC _n0
999			_c65769 _d65769