On spaces of periodic functions with wavelet transforms
DOI:
https://doi.org/10.5269/bspm.37637Keywords:
periodic functions, wavelet transform, Sobolev spaceAbstract
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 $B^\kappa_p([0,1]^n)$.References
1. K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Basel, (2001).
2. L. Hormander, The Analysis of Linear Partial Differential Operators II, Springer, Berlin (1983).
3. T. H. Koornwinder, Wavelets: An Elementary Treatment of Theory and Applications, World Scientific Pub Co Inc, Singapore, (1993).
4. R. S. Pathak, The wavelet transforms of distributions, Tohoku Math. J., vol. 49, 823-839, (2005).
5. R. S. Pathak : Wavelets in a generalized Sobolev space, Computers and Mathematics with Applications, vol. 49, 823-839, (2005).
6. 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).
7. 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).
8. 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).
9. R. S. Pathak, The Wavelet transform, Atlantis Press/ World Scientific, France, (2009).
10. S. Zaidman, Distributions and Pseudo-Differential Operators, Logman, Essex, England, (1991).
11. A. I. Zayed, Wavelet Transform of Periodic Generalized Functions, Journal of Mathematical analysis and application, 183, 391-412, (1994).
2. L. Hormander, The Analysis of Linear Partial Differential Operators II, Springer, Berlin (1983).
3. T. H. Koornwinder, Wavelets: An Elementary Treatment of Theory and Applications, World Scientific Pub Co Inc, Singapore, (1993).
4. R. S. Pathak, The wavelet transforms of distributions, Tohoku Math. J., vol. 49, 823-839, (2005).
5. R. S. Pathak : Wavelets in a generalized Sobolev space, Computers and Mathematics with Applications, vol. 49, 823-839, (2005).
6. 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).
7. 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).
8. 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).
9. R. S. Pathak, The Wavelet transform, Atlantis Press/ World Scientific, France, (2009).
10. S. Zaidman, Distributions and Pseudo-Differential Operators, Logman, Essex, England, (1991).
11. A. I. Zayed, Wavelet Transform of Periodic Generalized Functions, Journal of Mathematical analysis and application, 183, 391-412, (1994).
Downloads
Published
2020-10-08
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
