Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru
Dear authors!
Submission of all materials is carried out only electronically through Online Submission System in
personal account.
DOI: 10.23671/VNC.2016.4.5980
On Generalization of Fourier and Hartley Transforms for Some Quotient Class of sequences
Al-Omari S. K. Q.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4.
Abstract: In this paper we consider a class of distributions and generate two spaces of Boehmians for certain class of integral operators. We derive a convolution theorem and generate two spaces of Boehmians. The integral operator under concern is well-defined, linear and one-to-one in the class of Boehmians. An inverse problem is also discussed in some details.
1. Al-Omari S. K. Q., Loonker D., Banerji P. K., Kalla S. L. Fourier
sine (cosine) transform for ultradistributions and their extensions
to tempered and ultra Boehmian spaces, Integr. Transf. Spec. Funct.
2008, vol. 19, no. 6, pp. 453-462.
2. Al-Omari S. K. Q., Kilicman A. On diffraction Fresnel transforms
for Boehmians, Abstr. Appl. Anal., 2011, vol. 2011, 11 p.
(Article ID 712746).
3. Al-Omari S. K. Q. Hartley transforms on certain space of
generalized functions, Georgian Math. J., 2013, vol. 20, no. 3, pp.
415-426.
4. Al-Omari S. K. Q., Kilicman A. Note on Boehmians for class of
optical Fresnel wavelet transforms, J. Funct. Space Appl., 2012,
vol. 2012, pp. 1-13. (Article ID 405368; DOI:10.1155/2012/405368).
5. Al-Omari S. K. Q., Kilicman A. On generalized Hartley-Hilbert and
Fourier-Hilbert transforms, Adv. Diff. Equ., 2012, vol. 2012, no.
232, pp. 1-12. (DOI:10.1186/1687-1847-2012-232).
6. Al-Omari S. K. Q. On a generalized Meijer-Laplace transforms of
Fox function type kernels and their extension to a class of
Boehmians, Georgian Math. J., 2015. (In Press).
7. Al-Omari S. K. Q. Some characteristics of S transforms in a class
of rapidly decreasing Boehmians, J. Pseudo-Differ. Oper. Appl.,
2014, vol. 5, issu 4, pp. 527-537. (DOI:10.1007/s11868-014-0102-8).
8. Boehme T. K. The support of Mikusinski operators, Tran. Amer.
Math. Soc., 1973, vol. 176, pp. 319-334.
9. Banerji P. K., Al-Omari S. K. Q., Debnath L. Tempered
distributional Fourier sine (cosine) transform, Integr. Transf.
Spec. Funct., 2006, vol. 17, no. 11, pp. 759-768.
10. Millane R. P. Analytic properties of the Hartley transform and
their Applications, Proc. IEEE., 1994, Vol. 82, no. 3, pp. 413-428.
11. Nemzer D. \(S\)-asymptotic properties of Boehmians, Integr.
Transf. Spec. Funct., 2010, vol. 21, no. 7, pp. 503-513.
12. Nemzer D. A note on the convergence of a series in the space of
Boehmians // Bull. Pure Appl. Math. 2008. Vol. 2. P. 63-69.
13. Pathak R. S. Integral transforms of generalized functions and
their applications. Amsterdam: Gordon and Breach Science Publishers,
1997.
14. Mikusinski P. Convergence of Boehmians, Japanese J. Math.,
1983, Vol. 9, no. 1, pp. 159-179.
15. Sundararajan N. and Srinivas Y. Fourier-Hilbert versus
Hartley-Hilbert transforms with some geophysical applications, J.
Appl. Geophys, 2010, Vol. 71, no. 4, pp. 157-161.