A Class of Singular Integral Equation of Convolution Type with csc（τ-θ）Kernel

LI Ping-run

doi:10.13371/j.cnki.chin.q.j.m.2014.04.017

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 4: 620 - 626

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.017

A Class of Singular Integral Equation of Convolution Type with csc（τ-θ）Kernel

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School of Mathematical Sciences, Qufu Normal University

LI Ping-run(1966-), male, native of Yanzhou, Shandong, an associate professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function and singular integral equation.

Received date: 2013-09-16

Online published: 2020-11-27

Supported by

Supported by the Qufu Normal University Youth Fund(XJ201218)；

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Abstract

In this paper, we propose and discuss a class of singular integral equation of convolution type with csc（τ- θ） kernel in class L₂[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L₂[-π, π].

Key words： singular integral equation; convolution type; csc（τ- θ） kernel

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LI Ping-run . A Class of Singular Integral Equation of Convolution Type with csc（τ-θ）Kernel[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(4) : 620 -626 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.017

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