Related papers: Block Toeplitz Matrices: Multiplicative Properties
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…
In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices.…
A complete description of 4-by-4 matrices $\begin{bmatrix}\alpha I & C \\D & \beta I\end{bmatrix}$, with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is…
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…
Toeplitz matrices arise naturally in harmonic analysis, operator theory, and numerical analysis. In this note we investigate Toeplitz matrices whose coefficients depend on the matrix size through a scaled kernel $a_k=f(k/n)$. We show that…
This paper reviews some characterizations of positive matrices and discusses which lead to useful parametrizations. It is argued that one of them, which we dub the Schur-Constantinescu parametrization is particularly useful. Two new…
In this paper, we study the matrix period and the competition period of Toeplitz matrices over a binary Boolean ring $\mathbb{B} = \{0,1\}$. Given subsets $S$ and $T$ of $\{1,\ldots,n-1\}$, an $n\times n$ Toeplitz matrix $A=T_n\langle S ; T…
Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…
This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the…
We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the…
We characterize bounded and invertible Toeplitz products on vector weighted Bergman spaces of the unit polydisc. For our purpose, we will need the notion of B\'ekoll\'e-Bonami weights in several parameters.
This paper introduces the classically successful theory of Toeplitz operators on the Hardy space over the unit disk to a new domain in $\mathbb C^d$ -- the symmetrized polydisk.
We describe certain special consequences of certain elementary methods from group theory for studying the algebraic complexity of matrix multiplication, as developed by H. Cohn, C. Umans et. al. in 2003 and 2005. The measure of complexity…
For a given nonnegative integer alpha, a matrix A_{n} of size n is called alpha-Toeplitz if its entries obey the rule A_{n}=[a_{r-alpha*s}]_{r,s=0}^{n-1}. Analogously, a matrix A_{n} again of size n is called alpha-circulant if A_{n}=…
The paper establishes error orders for integral limit approximations to the traces of products of Toeplitz matrices generated by integrable real symmetric functions defined on the unit circle. These approximations and the corresponding…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral product complexes. Then we compute the universal algebra of polyhedral product complexes under certain split…
Products of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of L-functions in families with the same…
In this article we derive, using standard methods of Toeplitz theory, an asymptotic formula for certain large minors of Toeplitz matrices. D. Bump and P. Diaconis obtained the same asymptotics using representation theory, with an answer…
We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the…
We propose a new framework for matrix theories that are equivalent to field theories on a toroidal spacetime. The correspondence is accomplished via infinite Toeplitz matrices whose entries match the field degrees of freedom on an…