The solution of many problems in physics and engineering reduces ultimately to the solution of linear equations of the form Ra = m, where JR and m are given N x N and N x 1 matrices and a is to be determined. Here our concern is with the fact that it generally takes 0(N) computations (one computation being the multiplication of two real numbers) to do this, and this might be a substantial burde...

A directed Toeplitz graph T n s 1 , ⋯ k ; t l with vertices id="M4"> , id="M5"> 2 id="M6"> id="M7"> is a whose adjacency matrix matrix. In this paper, we investig...

One of the common strategies in the study of Toeplitz operators consists in selecting of various special symbol classes S ⊂ L∞ so that the properties of both the individual Toeplitz operators Ta, with a ∈ S, and of the algebra generated by such Toeplitz operators can be characterized. A motivation to study an algebra generated by Toeplitz operators (rather than just Toeplitz operators themselve...

and Applied Analysis 3 For commuting problem, in 1963, Brown and Halmos 2 showed that two bounded Toeplitz operators Tφ and Tψ on the classical Hardy space commute if and only if i both φ and ψ are analytic, ii both φ and ψ are analytic, or iii one is a linear function of the other. On the Bergman space of the unit disk, some similar results were obtained for Toeplitz operators with bounded har...

A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

2 Two-Toda lattice and reductions (Hänkel and Toeplitz) 17 2.1 Two-Toda on Moment Matrices and Identities for τ -Functions 18 2.2 Reduction to Hänkel matrices: the standard Toda lattice and a Virasoro algebra of constraints . . . . . . . . . . . . . . . . . 26 2.3 Reduction to Toeplitz matrices: two-Toda Lattice and an SL(2,Z)algebra of constraints . . . . . . . . . . . . . . . . . . . . . . 29...

We study Toeplitz operators on the Hardy spaces of connected compact abelian groups and of tube-type bounded symmetric domains. A representation theorem for these operators and for classes of abstract Toeplitz elements in C*-algebras is proved. This is used to give a unified treatment to index theory in this setting, and a variety of new index theorems are proved that generalize the Gohberg–Kre...

The preconditioned conjugate gradient method is employed to solve Toeplitz systems T n x = b where the generating functions of the n-by-n Toeplitz matrices T n are functions with zeros. In this case, circulant preconditioners are known to give poor convergence, whereas band-Toeplitz preconditioners only ooer linear convergence and can only handle real-valued functions with zeros of even orders....

A dynamical system is said to be coalescent if its only endomorphisms are automorphisms. The question whether there exist coalescent ergodic dynamical systems with positive entropy has not been solved so far and it seems to be difficult. The analogous problem in topological dynamics has been solved by Walters ([W]). His example, however, is not minimal. In [B-K2], a class of strictly ergodic (h...