Fractional Wavelet Frames in L2(ℝ)

被引：0
|
作者：
Firdous A. Shah
Lokenath Debnath
机构：
[1] University of Kashmir,Dept. of Mathematics
[2] University of Texas Rio Grande Valley (UTRVG),School of Mathematical and Statistical Sciences
来源：
Fractional Calculus and Applied Analysis | 2018年 / 21卷
关键词：
Primary 42C40; Secondary 42C15; 41A17; 46F12; 26A33; fractional wavelet; fractional Fourier transform; wavelet frame; fractional wavelet transform;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The objective of this paper is to construct fractional wavelet frames in L2(ℝ). A necessary condition and four sufficient conditions for fractional wavelet frames are given by virtue of fractional Fourier transform. The proposed inequalities generalize all the classical wavelet inequalities when θ = π/2. An example is presented at the end.
引用
收藏
页码：399 / 422
页数：23
相关论文
共 50 条
  • [41] Parseval frame wavelet multipliers in L2(ℝd)
    Zhongyan Li
    Xianliang Shi
    [J]. Chinese Annals of Mathematics, Series B, 2012, 33 : 949 - 960
  • [42] Parseval frame wavelet multipliers in L2(Rd)
    Li, Zhongyan
    Shi, Xianliang
    [J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2012, 33 (06) : 949 - 960
  • [43] Free metaplectic wavelet transform in L2(Rn)
    Shah, Firdous A.
    Qadri, Huzaifa L.
    Lone, Waseem Z.
    [J]. INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2022, 20 (04)
  • [44] Weyl-Heisenberg frames for subspaces of L2 (R)
    Casazza, PG
    Christensen, O
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (01) : 145 - 154
  • [45] On the Riesz bases, frames and minimal exponential systems in L2 [- π, π]
    Nakamura, Akihiro
    [J]. HOKKAIDO MATHEMATICAL JOURNAL, 2011, 40 (01) : 89 - 102
  • [46] Fractional wave packet systems in L2(R)
    Shah, Firdous A.
    Ahmad, O.
    Jorgensen, P. E.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (07)
  • [47] Time fractional linear problems on L2(Rd)
    Emamirad, Hassan
    Rougirel, Arnaud
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2018, 144 : 1 - 38
  • [48] On the stability of the L2 projection in fractional Sobolev spaces
    Steinbach, O
    [J]. NUMERISCHE MATHEMATIK, 2001, 88 (02) : 367 - 379
  • [49] Walsh Shift-Invariant Sequences and p-adic Nonhomogeneous Dual Wavelet Frames in L2 (R+)
    Zhang, Yan
    [J]. RESULTS IN MATHEMATICS, 2019, 74 (03)
  • [50] Dyadic bivariate wavelet multipliers in L2(R2)
    Li, Zhong Yan
    Shi, Xian Liang
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2011, 27 (08) : 1489 - 1500
12345