某些类具有反射与平移移位的卷积型奇异积分方程的解法

李平润

doi:10.13371/j.cnki.chin.q.j.m.2014.01.013

数学季刊 >

2014 , Vol. 29 >Issue 1: 107 - 115

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.01.013

某些类具有反射与平移移位的卷积型奇异积分方程的解法

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School of Mathematical Sciences, Qufu Normal University

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

收稿日期: 2011-09-19

网络出版日期: 2023-02-14

基金资助

Supported by the Qufu Normal University Youth Fund(XJ201218)

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The Method of Solutions for some Kinds of Singular Integral Equations of Convolution Type with Both Reflection and Translation Shift

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School of Mathematical Sciences, Qufu Normal University

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

Received date: 2011-09-19

Online published: 2023-02-14

Supported by

Supported by the Qufu Normal University Youth Fund(XJ201218)

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摘要

In this paper, some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform. In spite of the classical method for solution, we are to give another method, therefore the general solution and condition of solvability are obtained in class {0}.

关键词： singular integral equation; convolution type; Riemann boundary value problem; reflection; translation shift

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李平润 . 某些类具有反射与平移移位的卷积型奇异积分方程的解法[J]. 数学季刊, 2014 , 29(1) : 107 -115 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.01.013

Abstract

Key words： singular integral equation; convolution type; Riemann boundary value problem; reflection; translation shift

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