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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 1
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Research Article

Fractional biorthogonal wavelets in L2(ℝ)

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Pages 1-22 | Received 28 Jun 2020, Accepted 09 Jun 2021, Published online: 20 Jun 2021

References

  • Ozaktas H, Zalevsky Z, Kutay M. The fractional Fourier transform with applications in optics and signal processing. New York (NY): J. Wiley; 2001.
  • Wiener N. Hermitian polynomials and Fourier analysis. J Math Phys. 1929;8:70–73.
  • Namias V. The fractional order Fourier transform and its application to quantum mechanics. J Inst Math Appl. 1980;25:241–265.
  • McBride AC, Kerr FH. On Namias's fractional Fourier transforms. IMA J Appl Math. 1987;39:159–175.
  • Mendlovic D, Zalevsky Z, García J, et al. Fractional wavelet transform. Appl Opt. 1997;36:4801–4806.
  • Dai H, Zheng Z, Wang W. A new fractional wavelet transform. Commun Nonlinear Sci Numer Simulat. 2017;44:19–36.
  • Prasad A, Manna S, Mahato A, et al. The generalized continuous wavelet transform associated with the fractional Fourier transform. J Comput Appl Math. 2014;259:660–671.
  • Shah FA, Ahmad O, Jorgenson PE. Fractional wave packet frames in L2(R). J Math Phys. 2018;59:073509. DOI:10.1063/1.5047649.
  • Bownik M, Garrigos G. Biorthogonal wavelets, MRA's and shift-invariant spaces. Studia Math. 2004;160:231–248.
  • Cohen A, Daubechies I, Feauveau JC. Biorthogonal bases of compactly supported wavelets. Commun Pure Appl Math. 1992;45:485–560.
  • Chui CK, Wang JZ. On compactly supported spline wavelets and a duality principle. Trans Amer Math Soc. 1992;330(2):903–915.

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