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Research Article

Canonical potential and Lp-Sobolev space involving linear canonical Fourier transform

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Pages 295-315 | Received 01 Mar 2021, Accepted 25 Aug 2022, Published online: 12 Sep 2022

References

  • Collins SA. Lens-system diffraction integral written in terms of matrix optics. J Opt Soc Am. 1970;60(9):1168–1177.
  • Bernardo LM. ABCD matrix formalism of fractional Fourier optics. Opt Eng. 1996;35(3):732–740.
  • Abe S, Sheridan JT. Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation. Opt Lett. 1994;19(22):1801–1803.
  • James DFV, Agarwal GS. The generalized Fresnel transform and its applications to optics. Opt Commun. 1996;126(4–6):207–212.
  • Wolf KB. Construction and properties of canonical transforms. New York (NY): Plenum; 1979. Chapter 9, In integral transform in science and engineering.
  • Dhaouadi L, Sahbani J, Fitouhi A. Harmonic analysis associated to the canonical Fourier Bessel transform. Integral Transf Spec Funct. 2021;32(4):290–315.
  • Bultheel A, Marlinez-Sulbaran H. Recent development in the theory of the fractional Fourier and linear canonical transforms. Bull Belg Math Soc Simon Stevin. 2006;13(5):917–1005.
  • Prasad A, Kumar T. A pair of linear canonical Hankel transformations and associated pseudo-differential operators. Appl Anal. 2017;97(15):2727–2742.
  • Prasad A, Ansari ZA. Approximation of linear canonical wavelet transform on the generalized Sobolev spaces. J Pseudo-Differ Oper Appl. 2019;10(4):855–881.
  • Prasad A, Ansari ZA. Continuous wavelet transform involving linear canonical transform. Natl Acad Sci Lett. 2019;42(4):337–344.
  • Wei D, Ran Q, Li Y. A convolution and correlation theorem for the linear canonical transform and its application. Circ Syst Signal Process. 2012;31(1):301–312.
  • Wei D, Ran Q, Li Y. New convolution theorem for the linear canonical transform and its translation invariance property. Optik. 2012;123(16):1478–1481.
  • Deng B, Tao R, Wang Y. Convolution theorem for the linear canonical transform and their applications. Sci China Ser. 2006;49(5):592–603.
  • Zhang Z-C. New convolution and product theorem for the linear canonical transform and its applications. Optik. 2016;127(11):4894–4902.
  • Wong MW. Introduction to pseudo-differential operators. 3rd ed. Singapore: World Scientific; 2014.
  • Prasad A, Kumar P. Fractional wavelet transform in terms of fractional convolution. Prog Fract Differ Appl. 2015;3(1):201–210.
  • Guo Y. The linear canonical wavelet transform on some function spaces. Int J Wavelets Multiresol Inf Process. 2018;16(1):Article ID 1850010.
  • Pathak RS. Pseudo-differential operator associated with the Kontorovich–Lebedev transform. Invest Math Sci. 2015;5(1):29–46.
  • Pathak RS, Upadhyay SK. Pseudo-differential operators involving Hankel transforms. J Math Anal Appl. 1997;213(1):133–147.
  • Pathak RS, Pandey PK. Sobolev type spaces associated with Bessel operators. J Math Anal Appl. 1997;215(1):95–111.
  • Pathak RS, Upadhyay SK. Lμp-Boundedness of the pseudo-differential operator associated with the Bessel operator. J Math Anal Appl. 2001;257(1):141–153.
  • Salem NB, Dachraoui A. Sobolev type spaces associated with Jacobi differential operators. Integral Transf Spec Funct. 2000;9(3):163–184.
  • Prasad A, Mandal UK. The Kontorovich–Lebedev transform and Sobolev type space. Complex Anal Oper Theory. 2018;12(3):669–681.
  • Prasad A, Mandal UK, Verma SK. Zero-order Mehler–Fock transform and Sobolev-type space. Math Inequal Appl. 2019;22(2):761–775.
  • Pathak RS. A course in distribution theory and applications. New Delhi: Narosa Publishing House; 2009.

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