×

The wavelet transform of distributions. (English) Zbl 1078.42029

Author’s summary: “The continuous wavelet transform is extended to certain distributions and continuity results are obtained. Boundedness results in generalized Sobolev spaces, Besov spaces and Triebel-Lizorkin spaces are given”.
Reviewer: Qiyu Sun (Orlando)

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46F12 Integral transforms in distribution spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] C. K. Chui, Introduction to Wavelets, Academic Press, New York, 1992. · Zbl 0925.42016
[2] M. Holschneider, Wavelets, An Analysis Tool, Clarendon Press, Oxford, 1995. · Zbl 0874.42020
[3] A. C. McBride, Fractional Calculus and Integral Transforms of Generalized Functions, Pitman, London, 1979. · Zbl 0423.46029
[4] S. Moritoh, Wavelet transforms in Euclidian spaces—their relation with wavefront sets and Besov, Triebel-Zizorkin spaces, Tohoku Math. J. 47 (1995), 555–565. · Zbl 0843.35146 · doi:10.2748/tmj/1178225461
[5] R. S. Pathak, Integral Transforms of Generalized Functions and their Applications, Gordon and Breach Science Publishers, Amsterdam, 1997. · Zbl 0893.46035
[6] V. Perrier and C. Basdevant, Besov norms in terms of the continuous wavelet transform, Applications to structure functions, Math. Models Methods Appl. Sci. 6 (1996), 649–664. · Zbl 0978.42023 · doi:10.1142/S0218202596000262
[7] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, N.J., 1993. · Zbl 0821.42001
[8] E. M. Stein and G. Weiss, Fourier Analysis on Euclidian Spaces, Princeton University Press, Princeton, N.J., 1975.
[9] P. Tchamitchian, Wavelets, Functions, and Operators in Wavelets: Theory and Applications (ed. G. Erlebacher, M. Y. Hussainni and E. M. Jameson), 103–105, Oxford University, 1996. · Zbl 0887.42020
[10] H. Triebel, Theory of Function Spaces, Birkhauser-Verlag, Basel, 1983. · Zbl 0546.46027
[11] M. W. Wong, An Introduction to Pseudo-Differential Operators, World Scientific, Singapore, 1991. · Zbl 0753.35134
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.