Wavelets and Operators: Volume 1Cambridge University Press, 1992 - 223 pages Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase. |
Table des matières
Fourier series and integrals filtering and sampling | 1 |
Introduction | 18 |
Regularity of the function | 29 |
8 | 44 |
12 | 54 |
123 | 71 |
5 | 83 |
6 | 89 |
10 | 109 |
12345678 | 138 |
Wavelets and spaces of functions | 163 |
4 | 177 |
7 | 192 |
10 | 199 |
Holomorphic wavelets and Bochkarievs theorem | 202 |
New references on wavelets and their applications | 220 |
Autres éditions - Tout afficher
Expressions et termes fréquents
algebra analysis apply atoms Banach space bases belongs bounded calculate Chapter characterization compact support complete condition consider constant construct contained continuous converges corresponding cube decomposition decrease defined definition denote derivatives describe differentiable distributions dyadic equals equivalent example exists extend fact Finally finite Fourier series Fourier transform function function ƒ Further given gives H¹(R Hilbert Hölder identity inequality infinitely infinity integral interval L¹(R L²(R leads Lemma linear localization Math means measure multiresolution approximation norm observe obtained operator orthogonal orthonormal basis periodic precisely problem proof properties Proposition prove r-regular regularity remark replace restriction result satisfies sense sequence side simple suppose tends Theorem theory tion usual variable vector wavelet coefficients wavelet series write zero