Continuous wavelet transform on local fields
DOI :
https://doi.org/10.5269/bspm.v34i2.27340Résumé
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution are also studied.
Références
1. Daubechies,I, Ten Lectures on Wavelets ,CBMS/NSF Ser. Appl. Math., vol. 61, SIAM, (1992).
2. L. Debnath, Wavelet Transforms and Their Applications, Birkhauser, Boston, (2002).
3. C.K. Chui, An Introduction to Wavelets, Academic Press, 1992.
4. M. Holschneider, Wavelet analysis over Abelian groups, Appl. Comput. Harmon. Anal. 2, 52-60, (1995).
5. R. S. Pathak and Ashish Pathak . On convolution for wavelets transform , International journal of wavelets, multiresolution and information processing , 6(5): 739-747, (2008).
6. Ashish Pathak, P Yadav, M M Dixit, On convolution for general novel fractional wavelet transform , Journal of Advanced Research in Scientific Computing, 7(1), 30-37, (2015).
7. D. Ramakrishnan and R. J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics , Springer-Verlag, New York, 1999.
8. H. Jiang, D. Li and N. Jin, Multiresolution analysis on local fields, J. Math. Anal. Appl., 294 ,523- 532 , (2004.)
9. M.H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, 1975.
2. L. Debnath, Wavelet Transforms and Their Applications, Birkhauser, Boston, (2002).
3. C.K. Chui, An Introduction to Wavelets, Academic Press, 1992.
4. M. Holschneider, Wavelet analysis over Abelian groups, Appl. Comput. Harmon. Anal. 2, 52-60, (1995).
5. R. S. Pathak and Ashish Pathak . On convolution for wavelets transform , International journal of wavelets, multiresolution and information processing , 6(5): 739-747, (2008).
6. Ashish Pathak, P Yadav, M M Dixit, On convolution for general novel fractional wavelet transform , Journal of Advanced Research in Scientific Computing, 7(1), 30-37, (2015).
7. D. Ramakrishnan and R. J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics , Springer-Verlag, New York, 1999.
8. H. Jiang, D. Li and N. Jin, Multiresolution analysis on local fields, J. Math. Anal. Appl., 294 ,523- 532 , (2004.)
9. M.H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, 1975.
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Publié
2015-06-29
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Research Articles
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