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In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's $H$-function kernel. We employ a known differentiation formula of Fox's $H$-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.
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참고문헌 (19)
참고문헌 신청
S. K. Q. Al-Omari / 2017 / Estimation of the generalized Bessel-Struve transform in a certain space of generalized functions / Ukrain. Mat. Zh 69(9):1155~1165
S. K. Q. Al-Omari / 2016 / Boehmian spaces for a class of Whittaker integral transformations / Kuwait J. Sci 43(4):32~38
S. K. Q. Al-Omari / 2018 / Some remarks on short-time Fourier integral operators and classes of rapidly decaying functions / Math. Meth. Appl. Sci 41:1~8
S. K. Q. Al-Omari / 2018 / On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians / Georgian Math. J 25(1):1~8
S. K. Q. Al-Omari / 2015 / Some extensions of a certain integral transform to a quotient space of generalized functions / Open Math 13(1):816~825
S. K. Q. Al-Omari / 2016 / Boehmian spaces for a class of Whittaker integral transformations / Kuwait J. Sci 43(4):32~38
S. K. Q. Al-Omari / 2018 / Some remarks on short-time Fourier integral operators and classes of rapidly decaying functions / Math. Meth. Appl. Sci 41:1~8
S. K. Q. Al-Omari / 2018 / On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians / Georgian Math. J 25(1):1~8
S. K. Q. Al-Omari / 2015 / Some extensions of a certain integral transform to a quotient space of generalized functions / Open Math 13(1):816~825
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