Toeplitz CAR flows are a class of E0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always e...

We define the arithmetic self-similarity (AS) of a one-sided infinite sequence σ to be the set of arithmetic subsequences of σ which are a vertical shift of σ. We study the AS of several families of sequences, viz. completely additive sequences, Toeplitz words and Keane’s generalized Morse sequences. We give a complete characterization of the AS of completely additive sequences, and classify th...

Abstract. In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and this fixe...

Image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem, iterative methods have been shown to be effective. In this paper, we consider the case of a blurring function defined by space invariant and band-limited PSF, modeled by a linear system that has a band block Toeplitz structure with band Toeplitz blocks. In order...

The notion of an essentially slant Toeplitz operator on the space L is introduced and some of the properties of the set ESTO(L), the set of all essentially slant Toeplitz operators on L, are investigated. In particular the conditions under which the product of two operators in ESTO(L) is in ESTO(L) are discussed. The notion is generalized to kth-order essentially slant Toeplitz operators. The n...

In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This resul...

High Performance Algorithms for Toeplitz and block Toeplitz matrices

The Bareiss algorithm is one of the classical fast solvers for systems of linear equations with Toeplitz coeecient matrices. The method takes advantage of the special structure, and it computes the solution of a Toeplitz system of order N with only O(N 2) arithmetic operations, instead of O(N 3) operations. However, the original Bareiss algorithm requires that all leading principal sub-matrices...

This dissertation studies some matrix results and gives their generalizations in the context of semisimple Lie groups. The adjoint orbit is the primary object in our study. The dissertation consists of four chapters. Chapter 1 is a brief introduction about the interplay between matrix theory and Lie theory. In Chapter 2 we introduce some structure theory of semisimple Lie groups and Lie algebra...

The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...