95 research outputs found
Riemann-Hilbert problems for poly-Hardy space on the unit ball
In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP)
with a constant coefficients for the poly-Hardy space on the real unit ball in
higher dimensions. We first discuss the boundary behaviour of functions in the
poly-Hardy class. Then we construct the Schwarz kernel and the higher order
Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly-
Hardy class. Finally, we obtain explicit integral expressions for their solutions.
As a special case, monogenic signals as elements in the Hardy space over the
unit sphere will be reconstructed in the case of boundary data given in terms
of functions having values in a Clifford subalgebra. Such monogenic signals
represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane
One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels
This paper consists of two parts. In the first part we give a brief survey of results on Buschman–Erdélyi operators, which are transmutations for the Bessel singular operator. Main properties and applications of Buschman–Erdélyi operators are outlined. In the second part of the paper we consider multi-dimensional integral transforms of Buschman–Erdélyi type with Legendre functions in kernels. Complete proofs are given in this part, main tools are based on Mellin transform properties and usage of Fox H-functions
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