Results 91 to 100 of about 190 (139)
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Wiener-Hopf Integral Equations
2000The 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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Wiener-Hopf Integral Equations, Toeplitz Matrices and Linear Systems
1982This paper contains a new method to solve Wiener-Hopf integral equations, which employs explicitly connections with linear systems. These connections are based on a special exponential operator representation of the kernel of the integral equation whose Fourier transform is analytic on the real line and at infinity. With this approach explicit formulas
Bart, H., Gohberg, I., Kaashoek, M. A.
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The Wiener--Hopf Integral Equation in the Supercritical Case
Mathematical Notes, 2004The 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 \(R^+\).
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Nystrom-Product Integration for Wiener-Hopf Equations with Applications to Radiative Transfer
IMA Journal of Numerical Analysis, 1989This paper presents a numerical solution of the Wiener-Hopf integral equation \(u(x)-\int^{\infty}_{\beta}K(x-t)u(t)dt=f(x),\) where \(K(x)\) has logarithmic singularity at \(x=0\), and decays exponentially as \(| x| \to \infty\). An approximate solution \(u_ n\) is defined by introducing a mesh with \(n\) subintervals on \([0,\infty)\), and then ...
Graham, Ivan G., Mendes, Wendy R.
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A generalized approach to solving Fredholm and Wiener-Hopf integral equations
1970 IEEE Symposium on Adaptive Processes (9th) Decision and Control, 1970A generalized method is presented for the solution of Fredholm and Wiener-Hopf integral equations using the theory of distributions. By separating the integral through determination of the limits of integration, bounded linear differential operators may be defined which reduce the integral equation problem to one of solving a distributional ...
Raymond Bittel, Someshwar Gupta
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Approximate solution of Wiener-Hopf integral equations and its discrete counterparts
Computational Mathematics and Mathematical Physics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barseghyan, A. G., Engibaryan, N. B.
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Wiener — Hopf Integral Equations: Finite Section Approximation and Projection Methods
1985We consider the numerical solution of integral equations on the half-line by their finite-section approximation and by projection methods. Convergence results for the finite-section approximation are discussed, and are shown to be important in the analysis of the convergence of the projection method.
I. H. Sloan, A. Spence
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A generalized approach to solving Fredholm and Wiener-Hopf integral equations†
International Journal of Systems Science, 1972A generalized method is presented for the solution of Fredholm and Wiener-Hopf integral equations using the theory of distributions. By separating the integral through determination of the limits of integration, bounded linear differential operators may be defined which reduce the integral equation problem to one of solving a distributional ...
RAYMOND H. BITTELJ, SOMESHWAR C. GUPTA
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On Volterra and Wiener–Hopf Integral Operators and Corresponding Equations of the First Kind
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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CRITERIA FOR NORMAL SOLVABILITY OF SYSTEMS OF SINGULAR INTEGRAL EQUATIONS AND WIENER-HOPF EQUATIONS
Mathematics of the USSR-Sbornik, 1970Let be the unit circle and let () be the Hilbert space of vector functions with coordinates in .Theorem. Let , () be matrices with elements continuous on . In order for the singular integral operator , from to , to be normally solvable it is necessary and sufficient for the following two conditions to be satisfied: a) The rank of each of the matrices ...
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