Solvability theory of general characteristic singular integral equations with a Carleman fractional linear shift on the unit circle

2000 ◽  
pp. 207-249
Author(s):  
Georgii S. Litvinchuk
Keyword(s):  
Unit Circle ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
General Characteristic ◽  
Solvability Theory

scholarly journals Finite-part singular integral approximations in Hilbert spaces

2004 ◽  
Vol 2004 (52) ◽  
pp. 2787-2793
Author(s):  
E. G. Ladopoulos ◽  
G. Tsamasphyros ◽  
V. A. Zisis
Keyword(s):  
Unit Circle ◽  
Integral Equations ◽  
Singular Integral ◽  
Hilbert Spaces ◽  
Existence Theorems ◽  
Singular Integral Equations ◽  
Finite Part ◽  
Algebraic Equations ◽  
Integration Interval ◽  
Linear Algebraic Equations

Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.

scholarly journals Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case

2014 ◽  
Vol 13 (01) ◽  
pp. 1-21 ◽  
Author(s):  
L. P. Castro ◽  
E. M. Rojas ◽  
S. Saitoh ◽  
N. M. Tuan ◽  
P. D. Tuan
Keyword(s):  
Boundary Value Problems ◽  
Unit Circle ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Degenerate Kernel ◽  
Algebraic Equations ◽  
Explicit Formulas ◽  
Riemann Boundary ◽  
Linear Algebraic Equations

By means of Riemann boundary value problems and of certain convenient systems of linear algebraic equations, this paper deals with the solvability of a class of singular integral equations with rotations and degenerate kernel within the case of a coefficient vanishing on the unit circle. All the possibilities about the index of the coefficients in the corresponding equations are considered and described in detail, and explicit formulas for their solutions are obtained. An example of application of the method is shown at the end of the last section.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna
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