Factorization Theory for Wiener
نویسندگان
چکیده
A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained upon certain indices of the factorizations. Under such conditions, the one-sided and two-sided inverses of the operators in study are also obtained.
منابع مشابه
The Wiener-Hopf factorization
We give a description of the classical Wiener-Hopf factorization from the point of view of excursion theory concentrating mainly on the case of random walks as opposed to Lévy processes. The exposition relies primarily on the ideas of Greenwood and Pitman (1979, 1980).
متن کاملProbability Theory Exponential Functional of Lévy Processes: Generalized Weierstrass Products and Wiener-hopf Factorization
In this note, we state a representation of the Mellin transform of the exponential functional of Lévy processes in terms of generalized Weierstrass products. As by-product, we obtain a multiplicative Wiener-Hopf factorization generalizing previous results obtained by the authors in [14] as well as smoothness properties of its distribution. Résumé. Fonctionnelle exponentielle des processus de Lé...
متن کاملWIENER-HOPF FACTORIZATION IN THE INVERSE SCATTERING THEORY FOR THE n-D SCHRODINGER EQUATION
We study the n-dimensional Schrodinger equation, n 2 2, with a nonspherically symmetric potential in the class of Agmon's short range potentials without any positive energy bound states. We give sufficient conditions that guarantee the existence of a Wiener-Hopf factorization of the corresponding scattering operator. We show that the potential can be recovered from the scattering operator by so...
متن کاملar X iv : m at h / 05 11 12 7 v 1 [ m at h . FA ] 5 N ov 2 00 5 Factorization theory for Wiener - Hopf plus Hankel operators with almost periodic symbols
A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...
متن کاملSpitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options
TheWiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a Lévy process, such as the maximum, the minimum and hitting times. Here we propose a constructive procedur...
متن کامل