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Multiwavelets in the generalized Sobolev space

โœ Scribed by R.S. Pathak; Gireesh Pandey; Ryuichi Ashino

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
401 KB
Volume
55
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

A class of r -regular multiwavelets is introduced with appropriate notation and definitions in H ฯ‰ W (R n ). The oscillation properity of the orthonormal system is obtained. A multiresolution analysis for multiwavelets is defined in H ฯ‰ W (R n ). Orthonormality conditions for multiscaling functions and multiwavelets are obtained. A multiwavelet expansion formula of Riesz potentials is given.

๐Ÿ“œ SIMILAR VOLUMES

Wavelets in a generalized Sobolev space
Wavelets in a generalized Sobolev space
โœ R.S. Pathak ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 648 KB

The generalized Sobolev space H~(R ~) is defined as a generalization of the usual Sobolev space H~(I:t~). A multiresolution analysis for the generalized Sobolev space is developed. Wavelets orthogonal with respect to this space are constructed. Some interesting special cases are discussed. @

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We study some slight modifications of the class ฮฑ-AC n (โ„ฆ, R m ) introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. and Appl. 303 (2005) 119-134]. In particular we prove that the classes ฮฑ-AC n ฮป (โ„ฆ, R m ), 0 < ฮป < 1, introduced in [C. Di Bari, C. Vetro, A remark on