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Continuous and discrete Bessel wavelet transforms. (English) Zbl 1034.44004

The authors speak about the continuous and discrete wavelet transforms associated with the Bessel operator, which are defined and studied in the book of K. Trimèche [“Generalized harmonic analysis and wavelet packets” (2001; Zbl 0976.44009)]. The results presented in this paper are given in this book.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
65T60 Numerical methods for wavelets
65T50 Numerical methods for discrete and fast Fourier transforms

Citations:

Zbl 0976.44009
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Full Text: DOI

References:

[1] Chui, C. K., An Introduction to Wavelets (1992), Academic Press: Academic Press New York · Zbl 0925.42016
[2] A. Erdélyi (Ed.), Tables of Integral Transforms, Vol. II, McGraw-Hill, New York, 1954.; A. Erdélyi (Ed.), Tables of Integral Transforms, Vol. II, McGraw-Hill, New York, 1954.
[3] Haimo, D. T., Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116, 330-375 (1965) · Zbl 0135.33502
[4] Hirschman, I. I., Variation diminishing Hankel transforms, J. Anal. Math., 8, 307-336 (1960 1961)
[5] Trime’che, K., Generalized Wavelets and Hypergroups (1997), Gordon and Breach: Gordon and Breach Amsterdam
[6] Watson, G. N., A Treatise on the Theory of Bessel Functions (1958), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0849.33001
[7] Zemanian, A. H., Generalized Integral Transformations (1968), Interscience: Interscience New York · Zbl 0181.12701
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