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This article is cited in 1 scientific paper (total in 1 paper)
Real, complex and functional analysis
Application of integral transforms composition method (ITCM) to obtaining transmutations via integral transforms with Bessel functions in kernels
E. L. Shishkinaab, S. M. Sitnikb, I. Jebablic a Voronezh State University, 1, Universitetskaya pl., Voronezh, 394000, Russia
b Belgorod State National Research University (BelGU), 85, Pobeda str., Belgorod, 308015, Russia
c Faculty of Sciences of Tunis (FST), University of Tunis El Manar (UTM), 2092, Rue de Toléde, El Manar 1, Tunis, Tunisia
Abstract:
In this paper we apply the Integral Transforms Composition Method (ITCM) in order to derive compositions of integral transforms with Bessel functions in kernels, and obtain norm estimates and other properties of such composition transforms. Exactly, we consider transmutations which are compositions of classical Hankel and $Y$ integral transforms. Norms estimates in $L_2$ for these integral transforms with Bessel functions in kernels and their compositions are obtained. Also boundedness conditions for such transforms in weighted Lebesgue classes are proved. Classical integral transforms are used in this method as basic blocks. The ITCM and transmutations obtained by this method are applied to deriving connection formulas for solutions of singular differential equations.
Keywords:
Hankel transform, $Y$ transform, Integral Transforms Composition Method (ITCM), transmutations, Slater theorem, Bessel functions, Meijer $G$–function, hypergeometric functions, Mellin transform.
Received June 30, 2021, published August 18, 2021
Citation:
E. L. Shishkina, S. M. Sitnik, I. Jebabli, “Application of integral transforms composition method (ITCM) to obtaining transmutations via integral transforms with Bessel functions in kernels”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 884–900
Linking options:
https://www.mathnet.ru/eng/semr1408 https://www.mathnet.ru/eng/semr/v18/i2/p884
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