The Jacobi polynomials are defined as , Re ?, Re s> -1, where , k =1,2,3,….
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Riesz Potential With Logarithmic Kernel in Generalized Hölder Spaces: Theorems on Inversion and Isomorphisms
Boris Grigorievich Vakulov (Southern Federal University, Russia) and Yuri Evgenievich Drobotov (Southern Federal University, Russia)
Copyright: © 2021
|Pages: 22
DOI: 10.4018/978-1-7998-5083-0.ch014
Abstract
The multidimensional Riesz potential type operators are of interest within mathematical modelling in economics, mathematical physics, and other, both theoretical and applied, disciplines as they play a significant role for analysis on fractal sets. Approaches of operator theory are relevant to researching various equations, which are widespread in financial analysis. In this chapter, integral equations with potential type operators are considered for functions from generalized Hölder spaces, which provide content terminology for formalizing the concept of smoothness, briefly described in the presented chapter. Results on potentials defined on the unit sphere are described for convenience of the analysis. An inverse operator for the Riesz potential with a logarithmic kernel is carried out, and the isomorphisms between generalized Hölder spaces are proven.