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The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Loot Price: R4,513
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The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Series: Mathematics and Its Applications, 446
Expected to ship within 10 - 15 working days
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This book represents the first attempt at a unified picture for the
pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in
applications, its analysis and the different methods of filtering
it out. The analysis and filtering cover the familiar Gibbs
phenomenon in Fourier series and integral representations of
functions with jump discontinuities. In ad dition it will include
other representations, such as general orthogonal series
expansions, general integral transforms, splines approximation, and
continuous as well as discrete wavelet approximations. The mate
rial in this book is presented in a manner accessible to
upperclassmen and graduate students in science and engineering, as
well as researchers who may face the Gibbs phenomenon in the varied
applications that in volve the Fourier and the other approximations
of functions with jump discontinuities. Those with more advanced
backgrounds in analysis will find basic material, results, and
motivations from which they can begin to develop deeper and more
general results. We must emphasize that the aim of this book (the
first on the sUbject): to satisfy such a diverse audience, is quite
difficult. In particular, our detailed derivations and their
illustrations for an introductory book may very well sound repeti
tive to the experts in the field who are expecting a research
monograph. To answer the concern of the researchers, we can only
hope that this book will prove helpful as a basic reference for
their research papers."
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