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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 8, Pages 1484–1496 (Mi zvmmf4740)  
This article is cited in 1 scientific paper (total in 1 paper)

Inversion of a logarithmic operator defined on a regular set of arcs lying on a circle

A. S. Il'inskii, E. V. Chernokozhin

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
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Abstract: The theory of singular integral equations is used to derive simple inversion formulas for a logarithmic operator defined on a contour consisting of an arbitrary number of identical arcs lying on a circle at an equal angular spacing. The action of the inverse operator on trigonometric functions is calculated, and the moments of the inverse operator with trigonometric functions are found. Even simpler formulas are derived in the approximation of small arcs.
Key words: singular integral equations, logarithmic operator, operator with a logarithmic kernel, semi-inversion method.
Received: 14.11.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 8, Pages 1415–1428
DOI: https://doi.org/10.1134/S0965542509080119
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. S. Il'inskii, E. V. Chernokozhin, “Inversion of a logarithmic operator defined on a regular set of arcs lying on a circle”, Zh. Vychisl. Mat. Mat. Fiz., 49:8 (2009), 1484–1496; Comput. Math. Math. Phys., 49:8 (2009), 1415–1428
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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