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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 15
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Articles

A pair of linear canonical Hankel transformations and associated pseudo-differential operators

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Pages 2727-2742 | Received 16 Jan 2017, Accepted 28 Sep 2017, Published online: 12 Oct 2017

References

  • Collins Jr SA . Lens-system diffraction integral written in terms of matrix optics. J Opt Soc Am. 1970;60:1168–1177.
  • Moshinsky M , Quesne C . Oscillator systems. In: Proceedings 15th Solvay Conference on Physics. New York (NY): Gordon Breach Science; 1974.
  • Bernardo LM . ABCD matrix formalism of fractional Fourier optics. Opt Eng. 1996;35(3):732–740.
  • Pei SC , Ding JJ . Eigenfunctions of linear canonical transform. IEEE Trans Signal Process. 2002;50(1):11–26.
  • Bultheel A , Martínez-Sulbaran H . Recent developments in the theory of the fractional Fourier and linear canonical transforms. Bull Belg Math Soc Simon Stevin. 2007;13(5):971–1005.
  • Haldun Ozaktas M , Zalevsky Z , Alper Kutay M . The fractional Fourier transform with applications in optics and signal processing. New York (NY): Wiley; 2001.
  • Prasad A , Maurya PK . A couple of fractional powers of Hankel-type integral transformations and pseudo-differential operators. SeMA. 2017;74(2):181–211.
  • Malgonde SP . On the generalized Hankel type integral transformation of generalized functions. Indian J Pure Appl Math. 2000;31(2):197–206.
  • Malgonde SP , Debnath L . On Hankel type integral transformations of generalized functions. Integral Transforms Spec Funct. 2004;15(5):421–430.
  • Prasad A , Mahato K . Two variants of fractional powers of Hankel integral transforms of arbitrary order. Ann Univ Ferrara Sez VII Sci Mat. 2015;61(2):309–331.
  • Koh EL , Li CK . The Hankel transformation of Banach-space-valued generalized functions. Proc Amer Math Soc. 1993;119(1):153–163.
  • Koh EL , Li CK . On the inverse of the Hankel transform. Integral Transforms Spec Funct. 1994;2(4):279–282.
  • Pathak RS . Integral transforms of generalized functions and their applications. Amsterdam: Gordon Breach Science; 1997.
  • Zemanian AH . Generalized integral transforms. New York (NY): Interscience; 1968.
  • Prasad A , Kumar P . Composition of pseudo-differential operators associated with fractional Hankel-Clifford integral transformations. Appl Anal. 2016;95(8):1792–1807.
  • Pérez JM , Robayna MS . A pair of generalized Hankel-Clifford transformations and their applications. J Math Anal Appl. 1991;154(2):543–557.
  • Mendez JM . A mixed Parseval equation and the generalized Hankel transformations. Proc Amer Math Soc. 1988;102(3):619–624.
  • Linares M , Méndez Pérez JMR . A Hankel type integral transformation on certain space of distributions. Bull Calcutta Math Soc. 1991;83:447–456.
  • Torre A . Hankel type integral transforms and their fractionalization: a note. Integral Transforms Spec Funct. 2008;19(4):277–292.
  • Kohn JJ , Nirenberg L . An algebra of pseudo-differential operators. Comm Pure Appl Math. 1965;18(1–2):269–305.
  • Hörmander L . Pseudo-differential operators. Comm Pure Appl Math. 1965;18(3):501–517.
  • Wong MW . An introduction to pseudo-differential operators. Singapore: World Scientific; 1999.
  • Rodino L . Linear partial differential operators in Gevrey spaces. Singapore: World Scientific; 1993.
  • Pathak RS , Pandey PK . A class of pseudo-differential operators associated with Bessel operators. J Math Anal Appl. 1995;196(2):736–747.
  • Salem NB , Dachraoui A . Pseudo-differential operators associated with the Jacobi differential operator. J Math Anal Appl. 1998;220(1):365–381.
  • Prasad A , Kumar M . Product of two generalized pseudo-differential operators involving fractional Fourier transform. J Pseudo Differ Oper Appl. 2011;2(3):355–365.

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