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Al-Omari, S. K. Q.; Kılıçman, Adem

On the generalized Krätzel transform and its extension to Bohemian spaces. (English) Zbl 1470.44008

Abstr. Appl. Anal. 2013, Article ID 841585, 7 p. (2013).
Summary: We investigate the Krätzel transform on certain class of generalized functions. We propose operations that lead to the construction of desired spaces of generalized functions. The Krätzel transform is extended and some of its properties are obtained.

MSC:

44A40 Calculus of Mikusiński and other operational calculi
46F12 Integral transforms in distribution spaces
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\textit{S. K. Q. Al-Omari} and \textit{A. Kılıçman}, Abstr. Appl. Anal. 2013, Article ID 841585, 7 p. (2013; Zbl 1470.44008)
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References:

[1] Al-Omari, S. K. Q.; Kılıçman, A., Unified treatment of the Krätzel transformation for generalized functions, Abstract and Applied Analysis, 2013, (2013) · Zbl 1286.46045
[2] Krätzel, E., Eine Verallgemeinerung der Laplace- und Meijer-Transformation, Wissenschaftliche Zeitschrift der Friedrich-Schiller, 14, 369-381, (1965) · Zbl 0168.10204
[3] Cruz-Báez, D. I.; Rodríguez, J., The \(L_\nu^{(\rho)}\)-transformation on McBride’s spaces of generalized functions, Commentationes Mathematicae Universitatis Carolinae, 39, 3, 445-452, (1998) · Zbl 0971.44002
[4] Rao, G. L. N.; Debnath, L., A generalized Meijer transformation, International Journal of Mathematics and Mathematical Sciences, 8, 2, 359-365, (1985) · Zbl 0597.46036
[5] Zemanian, A. H., Generalized Integral Transformations, (1987), New York, NY, USA: Dover, New York, NY, USA · Zbl 0643.46029
[6] Karunakaran, V.; Chella Rajathi, R. A., Gelfand transform for a Boehmian space of analytic functions, Annales Polonici Mathematici, 101, 1, 39-45, (2011) · Zbl 1238.46044
[7] Beardsley, J.; Mikusiński, P., A sheaf of Boehmians, Annales Polonici Mathematici, 107, 3, 293-307, (2013) · Zbl 1275.46027
[8] Nemzer, D., One-parameter groups of Boehmians, Bulletin of the Korean Mathematical Society, 44, 3, 419-428, (2007) · Zbl 1144.46038
[9] Mikusiński, P., Fourier transform for integrable Boehmians, The Rocky Mountain Journal of Mathematics, 17, 3, 577-582, (1987) · Zbl 0629.44005
[10] Mikusiński, P., Tempered Boehmians and ultradistributions, Proceedings of the American Mathematical Society, 123, 3, 813-817, (1995) · Zbl 0821.46053
[11] Mikusiński, P., Convergence of Boehmians, Japanese Journal of Mathematics, 9, 1, 159-179, (1983) · Zbl 0524.44005
[12] Al-Omari, S. K. Q.; Kılıçman, A., On generalized Hartley-Hilbert and Fourier-Hilbert transforms, Advances in Difference Equations, 2012, (2012) · Zbl 1381.42006
[13] Boehme, T. K., The support of Mikusiński operators, Transactions of the American Mathematical Society, 176, 319-334, (1973) · Zbl 0268.44005
[14] Nemzer, D., Boehmians on the torus, Bulletin of the Korean Mathematical Society, 43, 4, 831-839, (2006) · Zbl 1132.46029
[15] Karunakaran, V.; Ganesan, C., Fourier transform on integrable Boehmians, Integral Transforms and Special Functions, 20, 11-12, 937-941, (2009) · Zbl 1191.42003
[16] Al-Omari, S. K. Q.; Kılıçman, A., Some remarks on the extended Hartley-Hilbert and Fourier-Hilbert transforms of Boehmians, Abstract and Applied Analysis, 2013, (2013) · Zbl 1275.42004
[17] Nemzer, D., A note on the convergence of a series in the space of Boehmians, Bulletin of Pure and Applied Mathematics, 2, 1, 63-69, (2008) · Zbl 1156.46305
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