Explicit Wiener-hopf Factorization for Certain Non-rational Matrix Functions
نویسندگان
چکیده
Explicit Wiener-Hopf factorizations are obtained for a certain class of nonrational 2 x 2 matrix functions that are related to the scattering matrices for the 1-D SchrSdinger equation. The diagonal elements coincide and are meromorphic and nonzero in the upperhalf complex plane and either they vanish linearly at the origin or they do not vanish. The most conspicuous nonrationality consists of imaginary exponential factors in the offdiagonal elements.
منابع مشابه
The Wiener--Hopf Technique for Impenetrable Wedges Having Arbitrary Aperture Angle
The diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener-Hopf (W-H) technique. A system of functional equations called generalized Wiener-Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle these equations are recognizable as standard or classical Wiener-Hopf equations (CWHE). However, in all cases, a mapping to a suit...
متن کاملFactorization of Block Triangular Matrix Functions with Off-diagonal Binomials
Factorizations of Wiener–Hopf type are considered in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups, with a non-archimedean linear order on the dual group. A criterion for factorizability is established for 2 × 2 block triangular matrix functions with elementary functions on the main diagonal and a binomial expression in the off-diagonal...
متن کاملAn Interpretation of Rosenbrock's Theorem Via Local Rings
the invariant factors of its state-space matrix A + BF . This result can be seen as the solution of an inverse problem; that of finding a non-singular polynomial matrix with prescribed in‐ variant factors and left Wiener–Hopf factorization indices at infinity. To see this we recall that the invariant factors form a complete system of invariants for the finite equivalence of polynomial matrices ...
متن کاملWiener-hopf Factorization and Distribution of Extrema for a Family of Lévy Processes
In this paper we introduce a ten-parameter family of Lévy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by the property that the characteristic exp...
متن کاملFinite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is a...
متن کامل