Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30075
On Fourier Type Integral Transform for a Class of Generalized Quotients

Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125119

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 778

References:


[1] V. K. Tuan and M. Saigo (1995), Convolution of Hankel transform and its application to an integral involving Bessel functions of first kind. Internat. J. Math. Math. Sci. 18(3), 545-550.
[2] N. Xuan Thao, V. K. Tuan and N. Minh Khoa (2004), A generalized convolution with a weight function for the Fourier cosine and sine Transformations, Fract. Cal.appl. Anal. 7(3), 323-337.
[3] K. N. Minh, V. A. Kakichev and V. K. (1998), Tuan. On the generalized convolution for Fourier cosine and sine transforms. East-West J. Math. 1(1) 85-90
[4] H. J. Glaeske and V. K. Tuan (1995), Some applications of the convolution theorem of the Hilbert transform. Integral Transforms and Special Functions 3(4) , 263-268.
[5] H. M. Srivastava and V. K. Tuan (1995), A new convolution theorem for the Stieltjes transform and its application to a class of singular integral equations. Arch. Math. 64(2) ,144-149.
[6] S. K. Q. Al-Omari and A. Kilicman (2012), On diffraction Fresnel transforms for Boehmians, Abstract and Applied Analysis, Volume 2011, Article ID 712746.
[7] S. K. Q. Al-Omari and Kilicman, A. (2013), An estimate of Sumudu transform for Boehmians, Advances in Difference Equations 2013, 2013:77.
[8] S. K. Q. Al-Omari (2013), Hartley transforms on certain space of generalized functions, Georg. Math. J. 20(3), 415-426.
[9] R. S. Pathak (1997). Integral transforms of generalized functions and their applications, Gordon and Breach Science Publishers, Australia , Canada, India, Japan.
[10] S. K. Q. Al-Omari (2014) ; Some characteristics of S transforms in a class of rapidly decreasing Boehmians, Journal of Pseudo-Differential Operators and Applications 01/2014; 5(4):527-537. DOI:10.1007/s11868-014-0102-8.
[11] N. Sundararajan and Y. Srinivas (2010) , Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications, Journal of Applied Geophysics 71,157-161.
[12] S. K. Q. Al-Omari and A. Kilicman (2012). Note on Boehmians for class of optical Fresnel wavelet transforms, Journal of Function Spaces and Applications, Volume 2012, Article ID 405368, doi:10.1155/2012/405368.
[13] S. K. Q. Al-Omari and A. Kilicman (2012) , On generalized Hartley-Hilbert and Fourier-Hilbert transforms, Advances in Difference Equations 2012, 2012:232 doi:10.1186/1687-1847-2012-232.
[14] S. K. Q. Al-Omari (2015), On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians. Georg. Math. J. To appear .
[15] S. K. Q. Al-Omari and Adam Kilicman (2013), Unified treatment of the Kratzel transformation for generalized functions, Abstract and Applied Analysis Volume 2013, Article ID 750524,1-6.
[16] V. Karunakaran and C. Ganesan (2009), Fourier transform on integrable Boehmians, Integral Transforms Spec. Funct. 20 , 937–941.
[17] D. Nemzer (2009), A note on multipliers for integrable Boehmians, Fract. Calc.Appl. Anal., 12 , 87–96.
[18] V. Karunakaran and C. Prasanna Devi (2010), The Laplace transform on a Boehmian space, Ann. Polon. Math., 97 , 151–157.
[19] C. Ganesan (2010), Weighted ultra distributions and Boehmians, Int. Journal of Math. Analysis, 4 (15), 703–712.