Some extensions of a certain integral transform to a quotient space of generalized functions
Shrideh K.Q. Al-Omari ; Jafar F. Al-Omari
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

In this paper, we establish certain spaces of generalized functions for a class of ɛs2,1 transforms. We give the definition and derive certain properties of the extended ɛs2,1 transform in a context of Boehmian spaces. The extended ɛs2,1 transform is therefore well defined, linear and consistent with the classical ɛs2,1 transforms. Certain results are also established in some detail.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:275968
@article{bwmeta1.element.doi-10_1515_math-2015-0075,
     author = {Shrideh K.Q. Al-Omari and Jafar F. Al-Omari},
     title = {Some extensions of a certain integral transform to a quotient space of generalized functions},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0075}
}
Shrideh K.Q. Al-Omari; Jafar F. Al-Omari. Some extensions of a certain integral transform to a quotient space of generalized functions. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0075/

[1] Al-Omari, S. K. Q., Hartley transforms on certain space of generalized functions, Georg. Math. J., 2013; 20(3), 415-426 | Zbl 1277.42003

[2] Al-Omari, S. K. Q., Kilicman, A., Note on Boehmians for class of optical Fresnel wavelet transforms, J. Funct. Spac. Applic., 2012, Article ID 405368, doi:10.1155/2012/405368, 1-13 [Crossref] | Zbl 1266.46030

[3] Al-Omari, S. K. Q., Kilicman, A., On generalized Hartley-Hilbert and Fourier-Hilbert transforms, Adva. Diff. Equ., 2012, 2012:232 doi:10.1186/1687-1847-2012-232, 1-12 [Crossref]

[4] Boehme, T. K., The support of Mikusinski operators, Trans. Amer. Math. Soc., 1973; 176, 319-334 | Zbl 0268.44005

[5] Al-Omari, S. K. Q., Kilicman, A., On diffraction Fresnel transforms for Boehmians, Abstr. Appli. Anal., 2011, Article ID 712746. 1-13 | Zbl 1243.46032

[6] Mikusinski, P., Zayed, A., The Radon transform of Boehmians, Amer. Math. Soc., 1993; 118.2/, 561-570 | Zbl 0774.44004

[7] Roopkumar, R., Generalized Radon transform, Rocky Mount. J. Math., 2006; 36(4), 1375-1390 | Zbl 1135.46020

[8] Brown, D., Dernek, N., Yürekli, O., Identities for the E2;1-transform and their applications, Appli. Math. Compu. 2007; 187, 1557-1566 | Zbl 1228.44001

[9] Zemanian, A. H., Distribution theory and transform analysis, Dover Publications, Inc., New York. First Published by McGraw-Hill, Inc. New York, 1965 | Zbl 0127.07201

[10] Karunakaran, V., Roopkumar, R., Operational calculus and Fourier transform on Boehmians, Colloq. Math., 2005; 102, 21-32 | Zbl 1079.46029

[11] Karunakaran, V., Vembu, R., Hilbert transform on periodic Boehmians, Houst. J. Math., 2003, 29 , 439-454 | Zbl 1040.44001

[12] Karunakaran, V., Vembu, R., On point values of Boehmians, Rocky Moun. J. Math., 2005, 35, 181-193 | Zbl 1088.44002

[13] Mikusinski, P., Convergence of Boehmians, Japan. J. Math., 1983, 9, 159-179 | Zbl 0524.44005

[14] Mikusinski, P., Fourier transform for integrable Boehmians, Rocky Mountain J. Math., 1987, 17, 577-582 | Zbl 0629.44005

[15] Mikusinski, P., Boehmians and generalized functions, Acta Math. Hungar., 1988, 51, 271-281. | Zbl 0652.44005

[16] Mikusinski, P., Tempered Boehmians and ultra distributions, Proc. Amer. Math. Soc., 1995, 123, 813-817 | Zbl 0821.46053

[17] Mikusinski, P., On flexibility of Boehmians, Integ. Trans. Spec. Funct. 4, 1996, 141-146 [Crossref] | Zbl 0863.44004

[18] Mikusinski, P., Boehmians and pseudoquotients, Appl. Math. Inf. Sci., 2011, 5, 192-204 | Zbl 1231.44003

[19] Mikusinski, J., Mikusinski, P., Quotients de suites et leurs applications dans l’anlyse fonctionnelle, C. R. Acad. Funct., 1994, 2, 219-230 | Zbl 0495.44006

[20] Nemzer, D., Periodic Boehmians, Int. J. Math. Math. Sci., 1989, 12, 685-692 [Crossref] | Zbl 0736.46041

[21] Al-Omari, S. K. Q., On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians, Bull. kore. Math. Soc., 2015, In Press.

[22] Al-Omari, S. K. Q., Agarwal, P., Some general properties of a fractional Sumudu transform in the class of Boehmians, Kuwait J. Scie. Engin., 2015, In Press.

[23] Kananthai, A., The distribution solutions of ordinary differential equation with polynomial coefficients, Southeast Asian Bulle. Math., 2001, 25, 129-134 | Zbl 1009.46024

[24] Loonker, D., Banerji, P. K., Solution of integral equations by generalized wavelet transform, Bol. Soc. Paran. Mat., 2015, 33.2/, 89-94 [Crossref]