A. Böttcher; S. M. Grudsky; I. M. Spitkovsky : Two papers on inverse problems for the partial indices of matrix functions

Author(s) :

A. Böttcher; S. M. Grudsky; I. M. Spitkovsky

Title :

Two papers on inverse problems for the partial indices of matrix functions

Electronic source:

application/pdf

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-34, 1998

Mathematics Subject Classification :

47B35 [ Toeplitz operators, etc. ]

47A53 [ (Semi-)Fredholm operators; index theories ]

47A68 [ Factorization theory of linear operators ]

Abstract :

We first show that if \kappa and \nu are given integers, then there exist matrix functions whose right and left total indices are just \kappa and \nu. In the second part we prove that given two vectors \varrho and \lambda of integers, there exist matrix functions which have a right Wiener-Hopf factorization in L^2 with the partial indices \varrho and a left Wiener-Hopf factorization on L^2 with the partial indices \lambda.

Keywords :

Toeplitz operator, Wiener-Hopf operator, Wiener-Hopf factorization, Matrix function, Partial indices

Language :

english

Publication time :

12/1998