Abstract
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 L2(ℝ).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bastin, F. and Laubin, P. (to appear). Regular compactly supported wavelets in Sobolev spaces, inDuke 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 fromL 2(ℝ) toH s(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), 38–40.
Author information
Authors and Affiliations
Additional information
Communicated by Paul L. Butzer
Rights and permissions
About this article
Cite this article
Bastin, F., Boigelot, C. Biorthogonal wavelets in Hm(ℝ). The Journal of Fourier Analysis and Applications 4, 749–768 (1998). https://doi.org/10.1007/BF02479678
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02479678