Results 171 to 180 of about 7,827 (194)

Extremum Problem for the Wiener–Hopf Equation

Ukrainian Mathematical Journal, 2000
Summary: The extremum problem for the Wiener-Hopf equation obtained by replacing the condition \(u(x)=0\), \(x < 0,\) by the condition of minimum of the quadratic functional of the function \(u(x)\exp(-x ...
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Wiener—Hopf Equations

1991
Wiener and Hopf1 used a novel technique to solve Milne’s equation, which comes up in the theory of radiative equilibrium of stellar atmospheres:
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Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities

Journal of Optimization Theory and Applications, 1999
A general kind of variational inequalities are considered. It is demonstrated that they are equivalent to general Wiener-Hopf equations. Moreover, some new algorithms to solve the general variational inequalities are introduced and their convergence is proved.
Noor, M. A., Al-Said, E. A.
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Forms of Wiener-Hopf equations

2014
This chapter discusses the different forms of Wiener-Hopf equations. Besides the classical Wiener-Hopf equations (CWHE), different functional equations may be classified as modified W-H equations and generalized W-H equations.
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A Probabilistic Look at the Wiener--Hopf Equation

SIAM Review, 1998
The Wiener-Hopf integral equation \[ Z(x)=z(x)+ \int^x_{-\infty} Z(x-y)F(dy), \quad x\geq 0, \] is analysed by purely probabilistic methods. The author investigates the nonnegative solutions \(Z\) of the equation assuming \(z\) to be nonnegative and bounded on finite intervals and \(F\) to be a probability measure with existing mean \(\mu\). He applies
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Numerical Solution of Mellin Type Equations via Wiener-Hopf Equations

2002
Recently the authors have proposed to replace the classical Gauss-Laguerre quadrature formula and its associated rules of product type by truncated versions of them, obtained by ignoring the last part of the nodes. This has the effect of getting optimal order of convergence using a significantly less number of nodes.
MASTROIANNI G, MONEGATO, Giovanni
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Wiener-Hopf equations technique for variational inequalities

Korean journal of computational & applied mathematics, 2000
Let \(H\) be a Hilbert space with the scalar product \(\langle\cdot,\cdot\rangle\), \(T:H\to H\), \(K\subset H\) be nonempty closed convex and let \(P_K\) denote the projection of \(H\) onto \(K\). Fix \(\rho>0\). The author shows the equivalence between the variational inequality \[ u\in K:\qquad\langle Tu,v-u\rangle \geq 0 \quad\forall v\in H \] and ...
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THE WIENER-HOPF EQUATION AND BLASCHKE PRODUCTS

Mathematics of the USSR-Sbornik, 1991
A Wiener-Hopf operator A is studied in the space of functions locally square-integrable on R and slowly increasing to ∞. The symbol of the operator is an infinitely differentiable function on R and has at ∞ a discontinuity of "vorticity point" type described either by a Blaschke function with all its zeros concentrated in a strip and bounded away from ...
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Wiener-Hopf Integral Equations, Toeplitz Matrices and Linear Systems

1982
This 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 EQUATION IN NEVANLINNA AND SMIRNOV ALGEBRAS

Mathematics of the USSR-Izvestiya, 1988
The author constructs a solution of the generalized Wiener-Hopf equation in Nevanlinna algebras \(N^{\pm}\) and Smirnov algebras \(N_*^{\pm}\). In addition the factorization problem and the Riemann-Hilbert boundary value problem in Smirnov algebras \(N_*^{\pm}\) are solved.
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