Wavelets for nonuniform non-stationary MRA on $H^s(\mathbb{K})$
DOI:
https://doi.org/10.5269/bspm.52573Abstract
In this paper, we are defined the nonuniform non-stationary multiresolution analysis (NUNSMRA) on Sobolev space over local fields ($H^s(\mathbb{K})$) and with help of NUNSMRA orthonormal wavelets are constructed.
References
1. H. Jiang, D. Li and N. Jin, Multiresolution analysis on local fields, J. Math. Anal. Appl. 294, 523-532, (2004). https://doi.org/10.1016/j.jmaa.2004.02.026
2. D. Ramakrishnan and R. J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics 186, SpringerVerlag, New York, (1999). https://doi.org/10.1007/978-1-4757-3085-2
3. M. H. Taibleson, Fourier Analysis on Local Fields, Mathematical Notes 15, Princeton University Press, Princeton, NJ, (1975).
4. Biswaranjan Behera and Qaiser Jahan, Multiresolution analysis on local fields and characterization of scaling functions, Adv. Pure Appl. Math. 3, 181-202, (2012). https://doi.org/10.1515/apam-2011-0016
5. Ashish Pathak, Continuous wavelet transform on local fields . Bol. Soc. Parana. Mat.,34(3) No.2, 113-121 , (2016). https://doi.org/10.5269/bspm.v34i2.27340
6. Ashish Pathak and Guru P. Singh, Wavelets in Sobolev space over loacl fields of positive characteristic, Int. Jou. of Wavelets Multuresolut Inf. Process., 16(4), (2018). https://doi.org/10.1142/S0219691318500273
7. Ashish Pathak, Dileep Kumar and Guru P. Singh, The Necessary Condition and Sufficient conditions for Wavelet Frames in Sobolev Space over Local field of Positive characteristic, Bol. Soc. Paran. Mat., 39(3)(2021) 81-92. https://doi.org/10.5269/bspm.40871
8. Ashish Pathak and Dileep Kumar, Characterization of Multiwavelets and MRA Wavelets in Hs (F), Int. J. Appl. Comput. Math. 5(6), 143, (2019). https://doi.org/10.1007/s40819-019-0725-9
9. Ashish Pathak and Guru P. Singh, Biorthogonal Wavelets in Sobolev Space Over Local Fields of Positive Characteristic, Int. J. Appl. Comput. Math. 6(2), 25, (2020). https://doi.org/10.1007/s40819-020-0782-0
10. Ashish Pathak and Guru P. Singh, Multilevel Wavelet Packet on Sobolev space over Local field of Positive Characteristic.(Communicated)
11. Ashish Pathak and Dileep Kumar, Multuresolution Analysis on Sobolev Space over Local fields of Positive Characteristic and Characterization of scaling function.(communicated ).
12. Ashish Pathak and Dileep Kumar, Existance of Unconditional Wavelet Bases for Lp- Norm over a Local Fields of positive Characteristic,(communicated ).
13. Shiva Mittal and Niraj K. Shukla, Generalized nonuniform multiresolution analyses, Colloq. Math. 153, 1, 121-147, (2018). https://doi.org/10.4064/cm6968-11-2016
14. Niraj K. Shukla, Saurabh Chandra Maury and Shiva Mittal, Semi-orthogonal Parseval wavelets associated with GMRAs on local fields of positive characteristic, Mediterr. J. Math. 16,no. 5, Art. 120, 20, (2019). https://doi.org/10.1007/s00009-019-1383-1
15. Nadya A. S. Atlouba, Shiva Mittal and Niraj K. Shukla, characterization of nonuniform multiwavelets using dimension function, Results Math. 72, 3, 1239-1255, (2017). https://doi.org/10.1007/s00025-016-0648-2
2. D. Ramakrishnan and R. J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics 186, SpringerVerlag, New York, (1999). https://doi.org/10.1007/978-1-4757-3085-2
3. M. H. Taibleson, Fourier Analysis on Local Fields, Mathematical Notes 15, Princeton University Press, Princeton, NJ, (1975).
4. Biswaranjan Behera and Qaiser Jahan, Multiresolution analysis on local fields and characterization of scaling functions, Adv. Pure Appl. Math. 3, 181-202, (2012). https://doi.org/10.1515/apam-2011-0016
5. Ashish Pathak, Continuous wavelet transform on local fields . Bol. Soc. Parana. Mat.,34(3) No.2, 113-121 , (2016). https://doi.org/10.5269/bspm.v34i2.27340
6. Ashish Pathak and Guru P. Singh, Wavelets in Sobolev space over loacl fields of positive characteristic, Int. Jou. of Wavelets Multuresolut Inf. Process., 16(4), (2018). https://doi.org/10.1142/S0219691318500273
7. Ashish Pathak, Dileep Kumar and Guru P. Singh, The Necessary Condition and Sufficient conditions for Wavelet Frames in Sobolev Space over Local field of Positive characteristic, Bol. Soc. Paran. Mat., 39(3)(2021) 81-92. https://doi.org/10.5269/bspm.40871
8. Ashish Pathak and Dileep Kumar, Characterization of Multiwavelets and MRA Wavelets in Hs (F), Int. J. Appl. Comput. Math. 5(6), 143, (2019). https://doi.org/10.1007/s40819-019-0725-9
9. Ashish Pathak and Guru P. Singh, Biorthogonal Wavelets in Sobolev Space Over Local Fields of Positive Characteristic, Int. J. Appl. Comput. Math. 6(2), 25, (2020). https://doi.org/10.1007/s40819-020-0782-0
10. Ashish Pathak and Guru P. Singh, Multilevel Wavelet Packet on Sobolev space over Local field of Positive Characteristic.(Communicated)
11. Ashish Pathak and Dileep Kumar, Multuresolution Analysis on Sobolev Space over Local fields of Positive Characteristic and Characterization of scaling function.(communicated ).
12. Ashish Pathak and Dileep Kumar, Existance of Unconditional Wavelet Bases for Lp- Norm over a Local Fields of positive Characteristic,(communicated ).
13. Shiva Mittal and Niraj K. Shukla, Generalized nonuniform multiresolution analyses, Colloq. Math. 153, 1, 121-147, (2018). https://doi.org/10.4064/cm6968-11-2016
14. Niraj K. Shukla, Saurabh Chandra Maury and Shiva Mittal, Semi-orthogonal Parseval wavelets associated with GMRAs on local fields of positive characteristic, Mediterr. J. Math. 16,no. 5, Art. 120, 20, (2019). https://doi.org/10.1007/s00009-019-1383-1
15. Nadya A. S. Atlouba, Shiva Mittal and Niraj K. Shukla, characterization of nonuniform multiwavelets using dimension function, Results Math. 72, 3, 1239-1255, (2017). https://doi.org/10.1007/s00025-016-0648-2
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2022-12-21
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Council of Scientific and Industrial Research, India
Grant numbers 09/013(0647)/2016 - EMR - 1
