Factorization of Almost Periodic Matrix Functions of Several Variables and Toeplitz Operators
نویسندگان
چکیده
We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toeplitz operators in terms of their symbols. In addition, we study stability of factorizations, and factorizations of hermitian valued almost periodic matrix functions of several variables.
منابع مشابه
Fredholmness and Invertibility of Toeplitz Operators with Matrix Almost Periodic Symbols
We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.
متن کاملMultiblock Problems for Almost Periodic Matrix Functions of Several Variables
In this paper we solve positive and contractive multiblock problems in the Wiener algebra of almost periodic functions of several variables. We thus generalize the classical four block problem that appears in robust control in many ways. The necessary and sufficient conditions are in terms of appropriate Toeplitz (positive case) and Hankel operators (contractive case) on Besikovitch space. In a...
متن کاملBlock Toeplitz Operators with Frequency- Modulated Semi-almost Periodic Symbols
This paper is concerned with the influence of frequency modulation on the semiFredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphism α of the real line that ensure the following: if b belongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix...
متن کاملAlgebras of Almost Periodic Functions with Bohr-fourier Spectrum in a Semigroup: Hermite Property and Its Applications
It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...
متن کاملSzegö limit theorems for operators with almost periodic diagonals Steffen
The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.
متن کامل