{"title":"On Fourier Type Integral Transform for a Class of Generalized Quotients","authors":"A. S. Issa, S. K. Q. AL-Omari","volume":113,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":279,"pagesEnd":284,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10004771","abstract":"In this paper, we investigate certain spaces of
\r\ngeneralized functions for the Fourier and Fourier type integral
\r\ntransforms. We discuss convolution theorems and establish certain
\r\nspaces of distributions for the considered integrals. The new Fourier
\r\ntype integral is well-defined, linear, one-to-one and continuous with
\r\nrespect to certain types of convergences. Many properties and an
\r\ninverse problem are also discussed in some details.","references":"[1] V. K. Tuan and M. Saigo (1995), Convolution of Hankel transform and its\r\napplication to an integral involving Bessel functions of first kind. Internat.\r\nJ. Math. Math. Sci. 18(3), 545-550.\r\n[2] N. Xuan Thao, V. K. Tuan and N. Minh Khoa (2004), A generalized\r\nconvolution with a weight function for the Fourier cosine and sine\r\nTransformations, Fract. Cal.appl. Anal. 7(3), 323-337.\r\n[3] K. N. Minh, V. A. Kakichev and V. K. (1998), Tuan. On the generalized\r\nconvolution for Fourier cosine and sine transforms. East-West J. Math.\r\n1(1) 85-90\r\n[4] H. J. Glaeske and V. K. Tuan (1995), Some applications of the convolution\r\ntheorem of the Hilbert transform. Integral Transforms and Special\r\nFunctions 3(4) , 263-268.\r\n[5] H. M. Srivastava and V. K. Tuan (1995), A new convolution theorem for\r\nthe Stieltjes transform and its application to a class of singular integral\r\nequations. Arch. Math. 64(2) ,144-149.\r\n[6] S. K. Q. Al-Omari and A. Kilicman (2012), On diffraction Fresnel\r\ntransforms for Boehmians, Abstract and Applied Analysis, Volume 2011,\r\nArticle ID 712746.\r\n[7] S. K. Q. Al-Omari and Kilicman, A. (2013), An estimate of Sumudu\r\ntransform for Boehmians, Advances in Difference Equations 2013,\r\n2013:77.\r\n[8] S. K. Q. Al-Omari (2013), Hartley transforms on certain space of\r\ngeneralized functions, Georg. Math. J. 20(3), 415-426.\r\n[9] R. S. Pathak (1997). Integral transforms of generalized functions and their\r\napplications, Gordon and Breach Science Publishers, Australia , Canada,\r\nIndia, Japan.\r\n[10] S. K. Q. Al-Omari (2014) ; Some characteristics of S\r\ntransforms in a class of rapidly decreasing Boehmians, Journal of\r\nPseudo-Differential Operators and Applications 01\/2014; 5(4):527-537.\r\nDOI:10.1007\/s11868-014-0102-8.\r\n[11] N. Sundararajan and Y. Srinivas (2010) , Fourier-Hilbert versus\r\nHartley-Hilbert transforms with some geophysical applications, Journal\r\nof Applied Geophysics 71,157-161.\r\n[12] S. K. Q. Al-Omari and A. Kilicman (2012). Note on Boehmians for\r\nclass of optical Fresnel wavelet transforms, Journal of Function\r\nSpaces and Applications, Volume 2012, Article ID 405368,\r\ndoi:10.1155\/2012\/405368.\r\n[13] S. K. Q. Al-Omari and A. Kilicman (2012) , On generalized\r\nHartley-Hilbert and Fourier-Hilbert transforms, Advances in Difference\r\nEquations 2012, 2012:232 doi:10.1186\/1687-1847-2012-232.\r\n[14] S. K. Q. Al-Omari (2015), On a class of generalized Meijer-Laplace\r\ntransforms of Fox function type kernels and their extension to a class of\r\nBoehmians. Georg. Math. J. To appear .\r\n[15] S. K. Q. Al-Omari and Adam Kilicman (2013), Unified treatment of the\r\nKratzel transformation for generalized functions, Abstract and Applied\r\nAnalysis Volume 2013, Article ID 750524,1-6.\r\n[16] V. Karunakaran and C. Ganesan (2009), Fourier transform on integrable\r\nBoehmians, Integral Transforms Spec. Funct. 20 , 937\u2013941.\r\n[17] D. Nemzer (2009), A note on multipliers for integrable Boehmians,\r\nFract. Calc.Appl. Anal., 12 , 87\u201396.\r\n[18] V. Karunakaran and C. Prasanna Devi (2010), The Laplace transform\r\non a Boehmian space, Ann. Polon. Math., 97 , 151\u2013157.\r\n[19] C. Ganesan (2010), Weighted ultra distributions and Boehmians, Int.\r\nJournal of Math. Analysis, 4 (15), 703\u2013712.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 113, 2016"}