Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions

2019 ◽  
Vol 344-345 ◽  
pp. 116-127 ◽  
Author(s):  
Pingrun Li
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Convolution Type ◽  
Cauchy Kernel ◽  
Increasing Functions

scholarly journals A convergence theorem for singular integral equations

1981 ◽  
Vol 22 (4) ◽  
pp. 539-552 ◽  
Author(s):  
David Elliott
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Singular Integral ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Convergence Theory ◽  
Cauchy Kernel ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

AbstractThe principal result of this paper states sufficient conditions for the convergence of the solutions of certain linear algebraic equations to the solution of a (linear) singular integral equation with Cauchy kernel. The motivation for this study has been the need to provide a convergence theory for a collocation method applied to the singular integral equation taken over the arc (−1, 1). However, much of the analysis will be applicable both to other approximation methods and to singular integral equations taken over other arcs or contours. An estimate for the rate of convergence is also given.

scholarly journals Singular Integral Equations of Convolution Type with Cosecant Kernels and Periodic Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pingrun Li
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Complex Analysis ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Convolution Type ◽  
Algebraic Equations ◽  
Periodic Coefficients ◽  
Linear Algebraic Equations ◽  
Classical Boundary

We study singular integral equations of convolution type with cosecant kernels and periodic coefficients in class L2[-π,π]. Such equations are transformed into a discrete jump problem or a discrete system of linear algebraic equations by using discrete Fourier transform. The conditions of Noethericity and the explicit solutions are obtained by means of the theory of classical boundary value problem and of the Fourier analysis theory. This paper will be of great significance for the study of improving and developing complex analysis, integral equations, and boundary value problems.

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