On Fredholm property of hypersingular integral operators in special classes of functions
- Authors: Smirnov Y.G.1
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Affiliations:
- Penza State University
- Issue: No 2 (2025)
- Pages: 3-14
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2072-3040/article/view/316340
- DOI: https://doi.org/10.21685/2072-3040-2025-2-1
- ID: 316340
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Abstract
Background. Hypersingular integral equations on a segment that arise in many issues of mathematical physics are considered. Materials and methods. Hypersingular equations are studied in special classes of functions, which are represented by Fourier series of Chebyshev polynomials of the 2nd kind. Results and conclusions. The criteria of compactness of operators in special classes of functions are proved. The main result is the proof of the Fredholm property of hypersingular operator in special classes of functions, which is important in the formulation and implementation of a numerical method for solving hypersingular equations.
About the authors
Yuriy G. Smirnov
Penza State University
Author for correspondence.
Email: mmm@pnzgu.ru
Doctor of physical and mathematical sciences, professor, head of the sub-department of mathematics and supercomputer modeling
(40 Krasnaya street, Penza, Russia)References
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