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- Title
On Solvability of the Sonin-Abel Equation in the Weighted Lebesgue Space.
- Authors
Kukushkin, Maksim V.
- Abstract
In this paper we present a method of studying a convolution operator under the Sonin conditions imposed on the kernel. The particular case of the Sonin kernel is a kernel of the fractional integral Riemman-Liouville operator, other various types of the Sonin kernels are a Bessel-type function, functions with power-logarithmic singularities at the origin e.t.c. We pay special attention to study kernels close to power type functions. The main our aim is to study the Sonin-Abel equation in the weighted Lebesgue space, the used method allows us to formulate a criterion of existence and uniqueness of the solution and classify a solution, due to the asymptotics of the Jacobi series coefficients of the right-hand side.
- Subjects
KERNEL (Mathematics); MORPHISMS (Mathematics); KERNEL functions; REPRODUCING kernel (Mathematics); JACOBI'S condition
- Publication
Fractal & Fractional, 2021, Vol 5, Issue 3, p1
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract5030077