On spaces of periodic functions with wavelet transforms
Abstract
Some boundedness results for the wavelet transform on $F_p([0,1]^n)$ and $F_p^*([0,1]^n)$, the spaces of periodic test functions, are obtained. The wavelet transform is also studied on generalized Sobolev space $B^\kappa_p([0,1]^n)$.Downloads
References
K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Basel, (2001).
L. Hormander, The Analysis of Linear Partial Differential Operators II, Springer, Berlin (1983).
T. H. Koornwinder, Wavelets: An Elementary Treatment of Theory and Applications, World Scientific Pub Co Inc, Singapore, (1993).
R. S. Pathak, The wavelet transforms of distributions, Tohoku Math. J., vol. 49, 823-839, (2005).
R. S. Pathak : Wavelets in a generalized Sobolev space, Computers and Mathematics with Applications, vol. 49, 823-839, (2005).
R. S. Pathak, S. K. Singh, The wavelet transform on spaces of type Lp, Advances in Algebra and Analysis, Vol. 1(3), 183-194, (2006).
R. S. Pathak, S. K. Singh, Boundedness of the wavelet transform in certain function spaces, J. Inequal. Pure Appl. Math., Vol. 8(1) , Article 23, (2007).
R. S. Pathak, Gireesh Pandey and Ryuichi Ashino, Multiwavelets in the generalized Sobolev space H!w (Rn), Computers and Mathematics with Applications, vol. 55, 423-440, (2008).
R. S. Pathak, The Wavelet transform, Atlantis Press/ World Scientific, France, (2009).
S. Zaidman, Distributions and Pseudo-Differential Operators, Logman, Essex, England, (1991).
A. I. Zayed, Wavelet Transform of Periodic Generalized Functions, Journal of Mathematical analysis and application, 183, 391-412, (1994).
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