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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 8, Pages 1484–1496 (Mi zvmmf4740)  

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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:8, 1415–1428

Bibliographic databases:

UDC: 519.634
Received: 14.11.2008

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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\paper Inversion of a~logarithmic operator defined on a~regular set of arcs lying on a~circle
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 49
\issue 8
\pages 1484--1496
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\pages 1415--1428
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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