Solution in closed form of an integral equation of convolution type in a hyperelliptic case
type: Item
instance of: scholarly article
title: Solution in closed form of an integral equation of convolution type in a hyperelliptic case
zbMATH Open document ID: 0961.45003
author: N. A. Degtyarenko
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: The author considers a Wiener-Hopf integral equation on the real line perturbed by terms with conjugation: \((\lambda_1+K_1)\theta_+\varphi+(\lambda_3+K_3)\theta_+\overline{\varphi} +(\lambda_2+K_2)\theta_-\varphi+(\lambda_4+K_4)\theta_-\overline{\varphi}=f(x)\), \(-\infty <x <\infty,\) where \((K_j\varphi)(x)=(K_j\ast\varphi)(x)\) and \(\theta_\pm (x)=\frac 12(1\pm \text{sign } x)\). Under some assumptions some cases are found when this equation may be solved in closed form.
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1541574
zbMATH Keywords: convolution-type integral equation
zbMATH Keywords: hyperelliptic case
zbMATH Keywords: solution in closed form
zbMATH Keywords: Wiener-Hopf integral equation
reviewed by: N. Karapetiants
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541574