TWO-DIMENTIONAL INTEGRAL TRANSFORM WITH THE MEIJER G-FUNCTION IN THE KERNEL IN THE SPACE OF SUMMABLE FUNCTIONS
Article Sidebar
Main Article Content
Abstract
Two-dimentional integral transform with the Meijer G-function in the kernel in the space of summable functions on a domain 
was studied. 
-theory of a considered integral transformation was constructed. Conditions for the boundedness and one-to-one operator of such a transformation from one -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.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Самко, С.Г. Интегралы и производные дробного порядка и некоторые их приложения / С.Г. Самко, А.А. Килбас, О.И. Маричев. – Минск : Наука и техника, 1987. – 688с.
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.
Most read articles by the same author(s)
- M. PAPKOVICH, O. SKOROMNIK, S. SHLAPAKOV, SOLUTION OF ONE CLASS OF MULTI-DIMENSIONAL INTEGRAL EQUATIONS OF THE FIRST KIND WITH HYPERBOLIC SINE FUNCTION IN KERNELS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 12 (2021)
- S. SITNIK, O. SKOROMNIK, Y. ARKHIPAVETS, ONE GENERALIZED H-TRANSFORMATION IN WEIGHT SPACES OF INTEGRATED FUNCTIONS ON A SEMI-AXIS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 12 (2021)
- S. SITNIK, O. SKOROMNIK, K. VASILEVICH, TWO-DIMENSIONAL INTEGRAL TRANSFORMATIONS WITH KUMMER FUNCTION AND HYPERGEOMETRIC GAUSSIAN FUNCTION IN KERNELS AS SPECIAL CASES OF TWO-DIMENSIONAL INTEGRAL G-TRANSFORMATION, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 1 (2023)
- S. SITNIK, O. SKOROMNIK, M. PAPKOVICH, TWO SPECIAL CASES OF TWO-DIMENSIONAL INTEGRAL G-TRANSFORMATION IN THE WEIGHTED SPACES OF SUMMABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 11 (2022)
- S. SITNIK, O. SKOROMNIK, M. PAPKOVICH, TWO-DIMENSIONAL INTEGRAL H-TRANSFORM IN WEIGHTED SPACES OF SUMMABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 2 (2023)
- O. SKOROMNIK, TWO-DIMENTIONAL INTEGRAL TRANSFORM WITH THE H-FUNCTION IN THE KERNEL IN THE SPACE OF SUMMABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 4 (2018)
- O. SKOROMNIK, T. ALEKSANDROVICH, SOLUTION OF A MULTIDIMENSIONAL INTEGRAL EQUATION OF THE FIRST KIND WITH THE BESSEL – KLIFFORD FUNCTION IN THE KERNEL OVER A PYRAMIDAL DOMAIN, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 4 (2015)
- O. SKOROMNIK, INTEGRAL TRANSFORMS WITH THE CONFLUENT HYPERDEOMETRIC FUNCTION OF KUMMER AND THE CUT BESSEL FUNCTION IN THE KERNELS AND INTEGRAL EQUATIONS OF THE FIRST KIND IN THE SPACE OF SUMMABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 12 (2016)
- O. SKOROMNIK, SOLUTION OF INTEGRAL EQUATIONS OF THE FIRST KIND WITH THE CONFLUENT HYPERDEOMETRIC FUNCTION AND NORMALIZED BESSEL FUNCTION IN THE KERNELS IN THE KLASS OF INTERGRABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 12 (2015)
- S. SITNIK, O. SKOROMNIK, A. KUROKHTINA, INTEGRAL TRANSFORMATION WITH THE MITTAG–LEFFLER FUNCTION IN SPACES OF LEBESGUE-MEASURABLE FUNCTIONS, Vestnik of Polotsk State University. Part C. Fundamental Sciences: No. 2 (2024)