Estimation of a modified integral associated with a special function kernel of Fox's $H$-function type
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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.
Abstract
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.
참고문헌 (19)
- S. K. Q. Al-Omari, "Estimation of the generalized Bessel-Struve transform in a certain space of generalized functions", Ukrain. Mat. Zh, 69(9), pp.1155~1165 (2017)[DOI]
- S. K. Q. Al-Omari, "Boehmian spaces for a class of Whittaker integral transformations", Kuwait J. Sci, 43(4), pp.32~38 (2016)
- S. K. Q. Al-Omari, "Some remarks on short-time Fourier integral operators and classes of rapidly decaying functions", Math. Meth. Appl. Sci, 41, pp.1~8 (2018)[DOI]
- S. K. Q. Al-Omari, "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), pp.1~8 (2018)[DOI]
- S. K. Q. Al-Omari, "Some extensions of a certain integral transform to a quotient space of generalized functions", Open Math, 13(1), pp.816~825 (2015)[DOI]
- S. K. Q. Al-Omari, "On the generalized Stieltjes transform of Fox’s kernel function and its properties in the space of generalized functions", J. Comput. Anal. Appl, 23(1), pp.108~118 (2017)
- S. K. Q. Al-Omari, "The extension of a modified integral operator to a class of generalized functions", J. Comput. Anal. Appl, 24(2), pp.209~218 (2018)
- R. Bhuvaneswari, "Boehmians of type S and their Fourier transforms", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 64(1), pp.27~43 (2010)
- B. L. J. Braaksma, "Asymptotic expansions and analytic continuations for a class of Barnes-integrals", Compositio Math, 15, pp.239~341 (1964)
- C. Fox, "The G and H functions as symmetrical Fourier kernels", Trans. Amer. Math. Soc, 98, pp.395~429 (1961)[DOI]
- A. A. Kilbas, "H-Transforms Theory and Applications" (2004), CRC Press Company
- S. Laurent, "Theorie des Distributions" (1951), Hermann and Cie
- A. M. Mathai, "The H-function" (2010), Springer
- P. Mikusinski, "Tempered Boehmians and ultradistributions", Proc. Amer. Math. Soc, 123(3), pp.813~817 (1995)[DOI]
- P. Mikusinski, "On flexibility of Boehmians", Integral Transform. Spec. Funct, 4(1-2), pp.141~146 (1996)[DOI]
- G. Murugusundaramoorthy, "A note on subclasses of starlike and convex functions associated with Bessel functions", J. Nonlinear Funct. Anal, 2014, pp.1~11 (2014)
- R. Roopkumar, "Stieltjes transform for Boehmians", Integral Transforms Spec. Funct, 18(11-12), pp.819~827 (2007)[DOI]
- H. M. Srivastava, "Some applications of higher-order derivatives involving certain subclass of analytic and multivalent functions", J. Nonlinear Var. Anal, 2, pp.343~353 (2018)
- A. H. Zemanian, "An Introduction to Generalized Functions, with Applications" (1965), McGraw-Hill Book Co