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Perturbation of wavelet frames on non-Archimedean fields | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 13، شماره 1، خرداد 2022، صفحه 197-208 اصل مقاله (428.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21909.2302 | ||
| نویسندگان | ||
| Ishtaq Ahmad* 1؛ Neyaz Ahmad2 | ||
| 1Department of Mathematics, Jammu and Kashmir Institute of Mathematical Sciences, Srinagar-190008, India | ||
| 2Department of Mathematics, National Institute of Technology, Srinagar-190006, India | ||
| تاریخ دریافت: 03 آذر 1399، تاریخ بازنگری: 01 بهمن 1399، تاریخ پذیرش: 14 اسفند 1399 | ||
| چکیده | ||
| The paper deals with two different aspects of wavelet frames. First, we obtain a necessary condition on irregular wavelet frames on local fields of positive characteristic and in the second aspect, we present some results on the perturbation of wavelet frames, when we disturb the mother function of a wavelet frame or dilation parameter. All the results have been carried without the compactness of support neither on generating function nor on its Fourier transform. | ||
| کلیدواژهها | ||
| Wavelet frames؛ Local fields؛ Perturbation | ||
| مراجع | ||
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[1] J. J. Benedetto, R.L. Benedetto, A wavelet theory for local fields and related groups, J. Geom. Anal. 14 (2004) 423–456. [2] O. Christensen, An Introduction to Frames and Riesz Bases, Springer, 2003. [3] O. Christensen and A. Rahimi, Frame properties of wave packet systems in L2 (Rd), Adv. Comput. Math. 29 (2008) 101-111. [4] F. Galindo and J. Sanz, Multiresolution analysis and Radon measures on a locally compact Abelian group, Czechoslovak Math. J., 51(4) (2001) 859–871. [5] S.F. Lukomskii, Multiresolution analysis on product of zero-dimensional Abelian groups, J. Math. Anal. Appl. 385 (2012) 1162–1178. [6] D. Ramakrishan and R.J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics, Springer, New York, 1999. [7] F. A. Shah and Abdullah, A characterization of tight wavelet frames on local fields of positive characteristic, J. Contemp. Math. Anal. 49(6) (2014) 251–259. [8] M.H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, 1975. | ||
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