Results 111 to 120 of about 133 (130)

Approximate factorization of Wiener–Hopf kernels

The Journal of the Acoustical Society of America, 2001
The key step in the solution of a Wiener–Hopf equation is the factorization of the Fourier transform of the kernel, K(α) (here, α is the Fourier variable). Exact factorizations are seldom useful, either because they do not exist or because they are too cumbersome to evaluate accurately.
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On Canonical Wiener-Hopf Factorizations

1999
This paper addresses some problems arising in Wiener-Hopf factorizations. The point of interest in this paper is not so much in the results which are slight generalizations of previous results, see Gohberg and Zucker [12, 13] and Zucker [18].
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Left Versus Right Wiener-Hopf Factorization

2002
In this chapter we show that if, Kland Krare the left and right total indices of some matrix function \(L_{N \times N}^\infty \) in with at most a finite number d of discontinuities on \(R \cup \left\{ \infty \right\}\) then \(\left| {{k_l} + {k_r}} \right|d\left( {N - 1} \right)\).
Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky   +2 more
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Wiener – hopf factorization revisited and some applications

Stochastics and Stochastic Reports, 1999
A reformulation of the classical Wiener-Hopf factorization for random walks is given; this is applied to the study of the asymptotic behaviour of the ladder variables, the distribution of the maximum and the renewal mass function in the bivariate renewal process of ladder times and ...
L. Alili, R. A. Doney
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A factorization procedure for Wiener-Hopf kernels

IEEE Transactions on Antennas and Propagation, 1969
This communication presents an integral representation for the Wiener-Hopf factorization of a class of functions of a complex variable in a form convenient for numerical processing. The representation is particularly suitable for radiation problems involving open waveguides or surface wave structures excited by waveguides when the waveguide dimensions ...
C. Bates, R. Mittra
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Commutative Wiener-Hopf factorization of a matrix

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1984
A class of n x n -matrices is given for which commutative Wiener-Hopf factorization is possible and the explicit factors are obtained. It is also shown that there are no other matrices with factors which commute if the factors possess distinct eigenvalues.
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Left Versus Right Canonical Wiener-Hopf Factorization

1986
In this paper the existence of a right canonical Wiener-Hopf factorization for a rational matrix function is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization.
Joseph A. Ball, André C. M. Ran
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Constructive Methods of Wiener-Hopf Factorization

1986
I: Canonical and Minimal Factorization.- Editorial introduction.- Left Versus Right Canonical Factorization.- 1. Introduction.- 2. Left and right canonical Wiener-Hopf factorization.- 3. Application to singular integral operators.- 4. Spectral and antispectral factorization on the unit circle.- 5.
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Canonical Wiener-Hopf Factorization via Corona Problems

2002
Explicit Wiener-Hopf factorization of matrix functions is a white whale of the theory of convolution type equations. Enormous effort has been spent on it but the cases when it has been found are still scarce. The Portuguese transformation and its applications (Chapters 13 14) can be thought of as results in this direction for triangular AP matrix ...
Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky   +2 more
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Wiener—Hopf Factorizations and the Recovery Problem

2003
In Chapter 7 we considered the recovery problem for unimodular functions. It is very important in applications to be able to solve the same problem for unitary-valued matrix functions. Namely, for a unitary-valued function U and a space X of functions on 𝕋 we consider in this chapter the problem of under which natural assumptions we can conclude that
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