On Fredholm property of hypersingular integral operators in special classes of functions
- Authors: Smirnov Y.G.1
-
Affiliations:
- Penza State University
- Issue: No 2 (2025)
- Pages: 3-14
- Section: MATHEMATICS
- URL: https://journal-vniispk.ru/2072-3040/article/view/316340
- DOI: https://doi.org/10.21685/2072-3040-2025-2-1
- ID: 316340
Cite item
Full Text
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
- Ilyinsky A.S., Smirnov Y.G. Electromagnetic Wave Diffraction by Conducting Screens. VSP, Utrecht, the Netherlands, 1998:114.
- Shestopalov Y.V., Smirnov Y.G., Chernokozhin E.V. Logarithmic Integral Equations in Electromagnetics. VSP, Utrecht, the Netherlands, 2000:117.
- Lifanov I.K., Poltavskii L.N., Vainikko M.M. Hypersingular Integral Equations and Their Applications. 1st ed. CRC Press, 2003:396.
- Setukha A.V. Metod integral'nykh uravneniy v matematicheskoy fizike: ucheb. posobie. = The method of integral equations in mathematical physics: textbook. Moscow: Izd-vo Mosk. un-ta, 2023:316. (In Russ.)
- Smirnov Yu.G. Matematicheskie metody issledovaniya zadach elektrodinamiki = Mathematical methods for studying problems of electrodynamics. Penza: Inf.-izd. tsentr PenzGU, 2009:268. (In Russ.)
- Suetin P.K. Klassicheskie ortogonal'nye mnogochleny = Classical orthogonal polynomials. Moscow: Nauka, 1979:416. (In Russ.)
- Teylor M. Psevdodifferentsial'nye operatory = Pseudodifferential operators. Moscow: Mir, 1985:472. (In Russ.)
- Lyuk Yu. Spetsial'nye matematicheskie funktsii i ikh approksimatsii = Special mathematical functions and their approximations. Moscow: Mir, 1980:608. (In Russ.)
- Trenogin V.A. Funktsional'nyy analiz = Functional analysis. Moscow: Nauka, 1980:440. (In Russ.)
Supplementary files
