Biorthogonal wavelets in H-m(R)

Bastin, Françoise; Boigelot, Christine

doi:10.1007/BF02479678

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Article (Scientific journals)

Biorthogonal wavelets in H-m(R)

Bastin, Françoise; Boigelot, Christine

1998 • In Journal of Fourier Analysis and Applications, 4 (6), p. 749-768

Peer reviewed

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https://hdl.handle.net/2268/28671

DOI
10.1007/BF02479678

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Keywords :

Riesz basis; wavelets; Sobolev spaces

Abstract :

[en] This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order. Using techniques of [1] and [2], the results presented here generalize to Sobolev spaces some constructions of Cohen et al. [7] and Chui and Wang [5] established in L-2(R).

Disciplines :

Mathematics

Author, co-author :

Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes

Boigelot, Christine

Language :

English

Title :

Biorthogonal wavelets in H-m(R)

Publication date :

1998

Journal title :

Journal of Fourier Analysis and Applications

ISSN :

1069-5869

eISSN :

1531-5851

Publisher :

Birkhauser Boston Inc, Cambridge, United Kingdom

Volume :

Issue :

Pages :

749-768

Peer reviewed :

Peer reviewed

Available on ORBi :

since 20 November 2009

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Bibliography

Bastin, F. and Laubin, P. (to appear). Regular compactly supported wavelets in Sobolev spaces, in Duke Math. J.
Bastin, F. and Laubin, P. (1997). Compactly supported wavelets in Sobolev spaces of integer order, App. Comp. Harmonic Anal., 4(1), 51-57.
Bastin, F. and Laubin, P. (1996). A walk in the theory of wavelets from L2(ℝ) to Hs(ℝ), Proc. Third Intl. Conf. Funct. Anal. Approx. Theory, Maratea, September.
Chui, C.K. (1992). An Introduction to Wavelets, Academic Press, New York.
Chui, C.K. and Wang, J.Z. (1992). On compactly supported spline wavelets and a duality principle, Trans. AMS, 330(2), 903-915.
Cohen, A. (1992). Ondelettes et traitement numérique du signal. Recherches en Mathématiques Appliquées, 25, Masson.
Cohen, A., Daubechies, I., and Feauveau, J.C. (1992). Biorthogonal basis of compactly supported wavelets, Comm. Pure Appl. Math., 45, 485-560.
Daubechies, I. (1988). Orthonormal basis of compactly supported wavelets, Comm. Pure Appl. Math., 41, 909-996.
Daubechies, I. (1992). Ten Lectures on wavelets, SIAM, CBMS61.
Meyer, Y. (1990). Ondelettes et opérateurs I: Ondelettes, Hermann.
Meyer, Y. (1994). Les ondelettes, algorithmes et applications, Armand Colin.
Micchelli, C. (1997). On a family of filters arising in wavelet construction, Appl. Comp. Harmonic Anal., 4(1), 38-50.