Nonuniform super wavelets in $L^2(\mathbb{K})$
Problemy analiza, Tome 11 (2022) no. 1, pp. 3-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce the structure of nonuniform super wavelets over local fields. We shall also provide the characterization of nonuniform parseval frame, nonuniform semi-orthogonal pareseval multiwavelets, and nonuniform super wavelets over local fields.
Keywords: nonuniform super wavelet, Local field, Parseval frame.
Mots-clés : Fourier transform
@article{PA_2022_11_1_a0,
     author = {O. Ahmad and Abdullah A. H. Ahmadini and M. Ahmad},
     title = {Nonuniform super wavelets in $L^2(\mathbb{K})$},
     journal = {Problemy analiza},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_1_a0/}
}
TY  - JOUR
AU  - O. Ahmad
AU  - Abdullah A. H. Ahmadini
AU  - M. Ahmad
TI  - Nonuniform super wavelets in $L^2(\mathbb{K})$
JO  - Problemy analiza
PY  - 2022
SP  - 3
EP  - 19
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_1_a0/
LA  - en
ID  - PA_2022_11_1_a0
ER  - 
%0 Journal Article
%A O. Ahmad
%A Abdullah A. H. Ahmadini
%A M. Ahmad
%T Nonuniform super wavelets in $L^2(\mathbb{K})$
%J Problemy analiza
%D 2022
%P 3-19
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_1_a0/
%G en
%F PA_2022_11_1_a0
O. Ahmad; Abdullah A. H. Ahmadini; M. Ahmad. Nonuniform super wavelets in $L^2(\mathbb{K})$. Problemy analiza, Tome 11 (2022) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/PA_2022_11_1_a0/

[1] Ahmad O., Bhat M. Y., Sheikh N. A., “Construction of Parseval Framelets Associated with GMRA on Local Fields of Positive Characteristic”, Numerical Functional Analysis and optimization, 2021 | DOI

[2] Ahmad O., Sheikh N. A., Shah F. A., “Fractional Multiresolution Analysis and Associated Scaling functions in $L^2(\mathbb R)$”, Analyis and Mathematical Physics, 11:47 (2021) | DOI

[3] Ahmad O., Sheikh N. A., “Novel Special Affine Wavelet transform and Associated Uncertainity Inequalities”, Int. Jour. of Geometric Methods in Mod. Phy., 24:4 (2021), 16 | DOI

[4] Ahmad O., Ahmad N., “Construction of Nonuniform Wavelet Frames on Non-Archimedean Fields”, Math. Phys. Anal. and Geom., 23:47 (2020)

[5] Ahmad O., Sheikh N. A., Nisar K. S., Shah F. A., “Biorthogonal Wavelets on Spectrum”, Math. Methods in Appl. Sci., 2021, 1–12 | DOI

[6] Ahmad O., Sheikh N. A., Ali M. A., “Nonuniform nonhomogeneous dual wavelet frames in Sobolev spaces in $L^2(\mathbb K)$”, Afrika Math., 31:7 (2020), 1145–1156 | DOI

[7] Benedetto J. J., Benedetto R. L., “A wavelet theory for local fields and related groups”, J. Geom. Anal., 14 (2004), 423–456

[8] Christensen O., An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2003

[9] Dai X., Larson D., Speegle D., “Wavelet sets in $\mathbb R^n$”, J. Fourier Anal. Appl., 3:4 (1997), 451–456

[10] Dai X., Diao Y., Gu Q., “On Super-Wavelets”, Oper. Theory Adv. Appl., 149, Birkhäuser, Basel, 2004, 153–165

[11] Duffin R. J., Shaeffer A. C., “A class of nonharmonic Fourier series”, Trans. Amer. Math. Soc., 72 (1952), 341–366

[12] Dutkay D. E., “Some equations relating multiwavelets and multiscaling functions”, J. Funct. Anal., 226:1 (2005), 1–20

[13] Dutkay D. E., and Jorgensen P., “Oversampling generates super-wavelets”, Proc. Amer. Math. Soc., 135:7 (2007), 2219–2227

[14] Daubechies I., Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics, SIAM, Philadelphia, 1992

[15] Gabardo J. P., Nashed M., “Nonuniform multiresolution analyses and spectral pairs”, J. Funct. Anal., 158 (1998), 209–241

[16] Gu Q., Han D., “Super-wavelets and decomposable wavelet frames”, J. Fourier Anal. Appl., 11:6 (2005), 683–696

[17] Shah F. A., Ahmad O., “Wave packet systems on local fields”, Journal of Geometry and Physics, 120 (2017), 5–18

[18] Shah F. A., Ahmad O., Rahimi A., “Frames Associated with Shift Invariant Spaces on Local Fields”, Filomat, 32:9 (2018), 3097–3110

[19] Shah F. A., Abdullah, “Nonuniform multiresolution analysis on local fields of positive characteristic”, Complex Anal. Opert. Theory, 9 (2015), 1589–1608

[20] Shukla N. K., Maury S. C., “Super-wavelets on local fields of positive characteristic”, Mathematische Nachrichten, 2017, 1–16

[21] Taibleson M. H., Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ, 1975

[22] Zhong-yan L., Xian-liang S., “On Parseval super-frame wavelets”, Appl. Math. J. Chinese. Univ. Ser. B, 27:2 (2012), 192–204