Abstract and Applied Analysis

Some Remarks on the Extended Hartley-Hilbert and Fourier-Hilbert Transforms of Boehmians

S. K. Q. Al-Omari and A. Kılıçman

Full-text: Open access

Abstract

We obtain generalizations of Hartley-Hilbert and Fourier-Hilbert transforms on classes of distributions having compact support. Furthermore, we also study extension to certain space of Lebesgue integrable Boehmians. New characterizing theorems are also established in an adequate performance.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 348701, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393448853

Digital Object Identifier
doi:10.1155/2013/348701

Mathematical Reviews number (MathSciNet)
MR3045072

Zentralblatt MATH identifier
1275.42004

Citation

Al-Omari, S. K. Q.; Kılıçman, A. Some Remarks on the Extended Hartley-Hilbert and Fourier-Hilbert Transforms of Boehmians. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 348701, 6 pages. doi:10.1155/2013/348701. https://projecteuclid.org/euclid.aaa/1393448853


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References

  • A. H. Zemanian, Generalized Integral Transformations, Dover Publications, New York, NY, USA, 2nd edition, 1987. \setlengthemsep1.5pt
  • R. S. Pathak, Integral Transforms of Generalized Functions and Their Applications, Gordon and Breach Science Publishers, North Vancouver, Canada, 1997.
  • S. K. Q. Al-Omari, D. Loonker, P. K. Banerji, and S. L. Kalla, “Fourier sine (cosine) transform for ultradistributions and their extensions to tempered and ultraBoehmian spaces,” Integral Transforms and Special Functions, vol. 19, no. 5-6, pp. 453–462, 2008.
  • S. Al-Omari and A. K\il\içman, “On the generalized Hartley-Hilbert and fourier-Hilbert transforms,” Advances in Difference Equations, vol. 2012, p. 232, 2012.
  • R. P. Millane, “Analytic properties of the Hartley transform and their applications,” Proceedings of the IEEE, vol. 82, no. 3, pp. 413–428, 1994.
  • N. Sundararajan and Y. Srinivas, “Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications,” Journal of Applied Geophysics, vol. 71, no. 4, pp. 157–161, 2010.
  • N. Sundarajan, “Fourier and hartley transforms: a mathematical twin,” Indian Journal of Pure and Applied Mathematics, vol. 8, no. 10, pp. 1361–1365, 1997.
  • T. K. Boehme, “The support of Mikusiński operators,” Transactions of the American Mathematical Society, vol. 176, pp. 319–334, 1973.
  • P. Mikusiński, “Fourier transform for integrable Boehmians,” The Rocky Mountain Journal of Mathematics, vol. 17, no. 3, pp. 577–582, 1987.
  • S. K. Q. Al-Omari and A. K\il\içman, “On diffraction Fresnel transforms for Boehmians,” Abstract and Applied Analysis, vol. 2011, Article ID 712746, 11 pages, 2011.
  • P. Mikusiński, “Tempered Boehmians and ultradistributions,” Proceedings of the American Mathematical Society, vol. 123, no. 3, pp. 813–817, 1995.
  • S. K. Q. Al-Omari and A. K\il\içman, “Note on Boehmians for class of optical Fresnel wavelet transforms,” Journal of Function Spaces and Applications, vol. 2012, Article ID 405368, 14 pages, 2012.