126
Views
1
CrossRef citations to date
0
Altmetric
Articles

On dual transform of fractional Hankel transform

ORCID Icon
Pages 1873-1893 | Received 20 May 2020, Accepted 11 Mar 2021, Published online: 05 Apr 2021

References

  • Namias V. Fractionalization of Hankel transforms. J Inst Math Appl. 1980;26(2):187–197.
  • Kerr FH. A fractional power theory for Hankel transforms. J Math Anal Appl. 1991;158:114–123.
  • Bracewell R. The Hankel transform. 3rd ed. New York: McGraw-Hill; 1999. p. 244–250. (The Fourier transform and its applications).
  • Karp DB. Fractional Hankel transformation and its applications in mathematical physics. Dokl Akad Nauk. 1994;338(1):10–14. [Russian Acad Sci Dokl Math. 1995;50(2):179–185.]
  • Krenk S. Some integral relations of Hankel transform type and applications to elasticity theory. Integr Equ Oper Theory. 1982;5(1):548–561.
  • Sheppard CJR, Larkin KG. Similarity theorems for fractional Fourier transforms and fractional Hankel transforms. Opt Commun. 1998;154:173–178.
  • Ünalmı Uzun B. Fractional Hankel and Bessel wavelet transforms of almost periodic signals. J Inequal Appl. 2015;388:12.
  • Elkachkouri A, Ghanmi A, Hafoud A. Bargmann's versus of the quaternionic fractional Hankel transform. J Appl Eng Math. 2020.
  • Elkachkouri A, Ghanmi A. The hyperholomorphic Bergman space on BR: integral representation and asymptotic behavior. Complex Anal Oper Theory. 2018;12(5):1351–1367.
  • Colombo F, Gonzàlez-Cervantes JO, Sabadini I. The Bergman-Sce transform for slice monogenic functions. Math. Methods Appl. Sci. 2011;34(15):1896–1909.
  • Colombo F, Gonzàlez-Cervantes JO, Sabadini I. On slice biregular functions and isomorphisms of Bergman spaces. Complex Var Elliptic Equ. 2012;57(7-8):825–839.
  • Benahmadi A, Ghanmi A. Dual of 2-D fractional Fourier transform associated to itô–Hermite polynomials. Res Math. 2020;75:168.
  • Andrews GE, Askey R, Roy R. Special functions. Cambridge: Cambridge University Press; 1999. (Encyclopedia of Mathematics and its Applications; vol. 71).
  • Colombo F, Sabadini I, Struppa DC. Noncommutative functional calculus, theory and applications of slice hyperholomorphic functions. Basel: Birkhäuser; 2011. (Progr. Math.; vol. 289).
  • Gentili G, Struppa DC. A new theory of regular functions of a quaternionic variable. Adv Math. 2007;216(1):279–301.
  • Gentili G, Stoppato C, Struppa DC. Regular functions of a quaternionic variable. Heidelberg: Springer; 2013. (Springer Monographs in Mathematics).
  • Alpay D, Bolotnikov V, Colombo F, et al. Interpolation problems for certain classes of slice hyperholomorphic functions. Integr Equ Oper Theory. 2016;86(2):165–183.
  • Alpay D, Colombo F, Sabadini I. Schur functions and their realizations in the slice hyperholomorphic setting. Integr Equ Oper Theory. 2012;72(2):253–289.
  • Alpay D, Colombo F, Sabadini I. Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions. J Anal Math. 2013;121:87–125.
  • Alpay D, Colombo F, Sabadini I. Slice hyperholomorphic Schur analysis. Cham: Birkhäuser-Springer; 2016. (Operator Theory: Advances and Applications; vol. 256).
  • Colombo F, Gonzàlez-Cervantes JO, Sabadini I. Further properties of the Bergman spaces of slice regular functions. Adv Geom. 2015;15(4):469–484.
  • Colombo F, Gonzàlez-Cervantes JO, Luna-Elizarrars ME, et al. On two approaches to the Bergman theory for slice regular functions. In: Advances in hypercomplex analysis. Milan: Springer; 2013. p. 39–54. (Springer INdAM Series; vol. 1).
  • Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm Pure Appl Math. 1961;14:187–214.
  • Magnus W, Oberhettinger F, Soni RP. Formulas and theorems in the special functions of mathematical physics. Berlin: Springer-Verlag; 1966.
  • Hsing T, Eubank R. Theoretical foundations of functional data analysis, with an introduction to linear operators. Chichester: John Wiley & Sons, Ltd.; 2015. (Wiley Series in Probability and Statistics).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.