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003 DE-He213
005 20160302165236.0
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008 120301s2009 fr | s |||| 0|eng d
020 _a9789491216244
_9978-94-91216-24-4
024 7 _a10.2991/978-94-91216-24-4
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aPathak, Ram Shankar.
_eauthor.
245 1 4 _aThe Wavelet Transform
_h[electronic resource] /
_cby Ram Shankar Pathak.
264 1 _aParis :
_bAtlantis Press,
_c2009.
300 _aXIII, 178p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAtlantis Studies in Mathematics for Engineering and Science,
_x1875-7642 ;
_v4
505 0 _aAn Overview -- TheWavelet Transform on Lp -- Composition ofWavelet Transforms -- TheWavelet Transform on Spaces of Type S -- The Wavelet Transform on Spaces of Type W -- The Wavelet Transform on a Generalized Sobolev Space -- A Class of Convolutions: Convolution for the Wavelet Transform -- The Wavelet Convolution Product -- Asymptotic Expansions of the Wavelet Transform when |b| is Large -- Asymptotic Expansions of the Wavelet Transform for Large and Small Values of a.
520 _aThe wavelet transform has emerged as one of the most promising function transforms with great potential in applications during the last four decades. The present monograph is an outcome of the recent researches by the author and his co-workers, most of which are not available in a book form. Nevertheless, it also contains the results of many other celebrated workers of the ?eld. The aim of the book is to enrich the theory of the wavelet transform and to provide new directions for further research in theory and applications of the wavelet transform. The book does not contain any sophisticated Mathematics. It is intended for graduate students of Mathematics, Physics and Engineering sciences, as well as interested researchers from other ?elds. The Fourier transform has wide applications in Pure and Applied Mathematics, Physics and Engineering sciences; but sometimes one has to make compromise with the results obtainedbytheFouriertransformwiththephysicalintuitions. ThereasonisthattheFourier transform does not re?ect the evolution over time of the (physical) spectrum and thus it contains no local information. The continuous wavelet transform (W f)(b,a), involving ? wavelet ?, translation parameterb and dilation parametera, overcomes these drawbacks of the Fourier transform by representing signals (time dependent functions) in the phase space (time/frequency) plane with a local frequency resolution. The Fourier transform is p n restricted to the domain L (R ) with 1 p 2, whereas the wavelet transform can be de?ned for 1 p.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aNumerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
830 0 _aAtlantis Studies in Mathematics for Engineering and Science,
_x1875-7642 ;
_v4
856 4 0 _uhttp://dx.doi.org/10.2991/978-94-91216-24-4
912 _aZDB-2-SMA
999 _c189024
_d189024