Solvability of a class of Wiener-Hopf integral equations
type: Item
instance of: scholarly article
title: Solvability of a class of Wiener-Hopf integral equations
zbMATH Open document ID: 0877.45003
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1997-08-05T00:00:00Z
review text: The author studies the solvability problem for Wiener-Hopf equation with symbol \[ A(\lambda)=\Biggl({\lambda\over\lambda+ i}\Biggr)^jB(\lambda), \] where \(A(\lambda)\), \(B(\lambda)\in{\mathcal F}\), the algebra of functions of the form \(A(\lambda)= c+\int^\infty_{-\infty}k(t)e^{i\lambda t}dt\), \(k(t)\in L_1(R^1)\), and \(j\) is some natural number. He establishes the connection between the first- and second-order moments of the kernel \(k(t)\) and properties of the symbol and gives a formula for the general solution of the renewal equation in \(E^+= L_p\), \(1\leq p<\infty\), \(M= L_\infty\), \(C\), \(C_0\).
reviewed by: N. Karapetiants
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1043217
zbMATH Keywords: solvability
zbMATH Keywords: Wiener-Hopf equation
zbMATH Keywords: symbol
zbMATH Keywords: general solution
zbMATH Keywords: renewal equation
author: G. A. Grigorian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1043217