TWO-DIMENTIONAL INTEGRAL TRANSFORM WITH THE MEIJER G-FUNCTION IN THE KERNEL IN THE SPACE OF SUMMABLE FUNCTIONS

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Published: Apr 15, 2019
Keywords:
two-dimensional integral G-transform, Meijer G-function, two-dimensional Mellin transform, the space of integrable functions, fractional integrals and derivatives двумерное интегральное G-преобразование, G-функция Мейера, двумерное преобразование Меллина, пространство интегрируемых функций, дробные интегралы и производные

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PAPKOVICH PAPKOVICH
Polotsk State University
O. SKOROMNIK
Polotsk State University

Abstract

Two-dimentional integral transform with the Meijer G-function in the kernel in the space of summable functions on a domain https://journals.psu.by/public/site/images/admin-situ/c-2019-4-1.jpg was studied. https://journals.psu.by/public/site/images/admin-situ/c-2019-4-2.jpg -theory of a considered integral transformation was constructed. Conditions for the boundedness and one-to-one operator of such a transformation from one https://journals.psu.by/public/site/images/admin-situ/c-2019-4-2.jpg -space to another were given, an analogue of the integration formula in parts was proved, various integral representations for the transformation under consideration were established. The results generalize the well know findings for corresponding one-dimentional integral transform.

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How to Cite
PAPKOVICH, P., & SKOROMNIK, O. (2019). TWO-DIMENTIONAL INTEGRAL TRANSFORM WITH THE MEIJER G-FUNCTION IN THE KERNEL IN THE SPACE OF SUMMABLE FUNCTIONS. Vestnik of Polotsk State University. Part C. Fundamental Sciences, (4), 131-136. Retrieved from https://journals.psu.by/fundamental/article/view/417
Issue
No. 4 (2019)
Section
mathematics
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This work is licensed under a Creative Commons Attribution 4.0 International License.

Author Biography

O. SKOROMNIK, Polotsk State University

канд. физ.-мат. наук, доц.

References

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Kilbas, A.A. H-Transforms. Theory and Applications / A.A. Kilbas, M.H. Saigo. – London [etc.] : Chapman and Hall. CRC Press, 2004. – 401 p.

Kilbas, A.A. Theory and applications of fractional differential equations. North – Holland Mathematics Studies 204 / A.A. Kilbas, H.M. Srivastava, J.J. Trujillo. – Amsterdam : Elsevier.xv, 2006. – 523 p.