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The Wiener--Hopf Integral Equation in the Supercritical Case

Mathematical Notes, 2004
The author studies an asymptotic behavior of the solutions of the homogeneous Wiener-Hopf integral equation \(S(x)=\int_0^\infty K(x-t)S(t) \,dt\), \(x>0,\) with smooth nonnegative even kernel \(K(x)\) such that \(K^{\prime}(x)\leq 0, K^{\prime\prime}(x)\geq 0,\) and \(K^{\prime\prime}(x) \downarrow \) on \(R^+\).
L. G. Arabadzhyan
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A Wiener-Hopf integral equation arising in some inference and queueing problems

Biometrika, 1974
SUMMARY The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails.
C. Atkinson
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Approximate solution of Wiener-Hopf integral equations and its discrete counterparts

Computational Mathematics and Mathematical Physics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barseghyan, A. G., Engibaryan, N. B.
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SYSTEMS OF WIENER-HOPF INTEGRAL EQUATIONS, AND NONLINEAR FACTORIZATION EQUATIONS

Mathematics of the USSR-Sbornik, 1985
Translation from Mat. Sb., Nov. Ser. 124(166), No.2(6), 189-216 (Russian) (1984; Zbl 0566.45007).
Engibaryan, N. B., Arabadzhyan, L. G.
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Stochastic Iterative Learning Control for Lumped- and Distributed-Parameter Systems: A Wiener-Filtering Approach

IEEE Transactions on Automatic Control, 2021
This article presents a stochastically optimal iterative learning control (ILC) approach by designing a general integral learning operator which minimizes the expected mean-squares output error.
A. Deutschmann‐Olek, G. Stadler, A. Kugi   +2 more
semanticscholar   +1 more source

GENERALIZED WIENER–HOPF EQUATIONS WITH DIRECTLY RIEMANN INTEGRABLE INHOMOGENEOUS TERM

Journal of Mathematical Sciences, 2023
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Wiener-Hopf Integral Equations

2000
The purpose of this chapter is to study the distributional solution of the integral equations of the type $$g(x) + \lambda \int_{0}^{\infty } {k(x - y)g(y)dy = f(x), x \geqslant 0}$$ (8.1) , as well as the corresponding equations of the first kind, the so-called Wiener-Hopf integral equations.
Ricardo Estrada, Ram P. Kanwal
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Fast Preconditioned Conjugate Gradient Algorithms for Wiener–Hopf Integral Equations

SIAM Journal on Numerical Analysis, 1994
Summary: The authors study circulant approximations of finite sections of a Wiener-Hopf integral equation on the half-line. Such circulant operators are defined by periodic kernel functions. They approximate finite sections of the Wiener-Hopf operator within a sum of a small operator and an operator with fixed finite rank.
Gohberg, Israel, Koltracht, Israel, Hanke, Martin   +2 more
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Circulant integral operators as preconditioners for Wiener-Hopf equations

Integral Equations and Operator Theory, 1995
The authors study the solution of the Wiener-Hopf equation \((\sigma I + K) x = g\), where the integral operator \((Kx)(t) = \int^\infty_0 k(t - s) x(s) ds\) is self adjoint and positive definite, \(k \in L_1(- \infty, \infty)\), \(g \in L_2(0,\infty)\), \(\sigma > 0\), by the preconditioned conjugate gradient method. A scheme of constructing circulant
Chan, Raymond H., Jin, Xiao-Qing, Ng, Michael K.   +2 more
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