Related papers: Otto Toeplitz: Algebraiker der unendlichen Matrize…
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 study Toeplitz operator theory on the doubling Fock spaces, which are Fock spaces whose exponential weight is associated to a subharmonic function with doubling Riesz measure. Namely, we characterize the boundedness, compactness and…
The classification of maximal left algebras of quaternion Toeplitz matrices is a harder problem that has received little attention up to now. In this paper, we introduce certain families of maximal left algebras of Toeplitz matrices with…
Based on a question raised by N. Feldman we discuss the dynamics of tuples of upper triangular Toeplitz matrices over $\mathbb{C}$. Some open problems are posed.
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval. In this work we get a deep link between (--$\Delta$) $\alpha$ ]0,1[ the fractional Laplacian on the interval ]0, 1[ and T N ($\Phi$ $\alpha$) the Toeplitz…
Toeplitz matrices are characterized by their constant diagonals, have been extensively studied in various settings, including over real and complex numbers. However, their study over quaternions is quite sparse. In this paper, we…
We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of…
In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in…
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input…
We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson…
G\"unter Hellwig was the author of influential textbooks on PDEs and differential operators of mathematical physics, an enthusiastic and inspiring teacher to generations of engineers, organiser of PDE conferences at Oberwolfach and a…
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…
The maximal commutative subalgebras containing only Toeplitz matrices have been identified as generalized circulants. A similar simple description cannot be obtained for block Toeplitz matrices. We introduce and investigate certain families…
This is an English translation of Felix Klein's paper "Ueber die Transformation elfter Ordnung der elliptischen Functionen" from 1879.
A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected set of these developments. Some new proofs are provided.
In this paper we give a short biography of Harald Niederreiter and we spotlight some cornerstones from his wide-ranging work. We focus on his results on uniform distribution, algebraic curves, polynomials and quasi-Monte Carlo methods. In…
In this note we discover and prove some interesting and important relations among sub-matrices of Sylvester matrices and triangular toeplitz matrices. The main result is Hill's identity discovered by R. D. Hill which has an important…
In this paper, we find the coefficient bounds using symmetric Toeplitz determinants for the functions belonging to the subclass $R(q)$.
Starting from a doubly infinite sequence of complex numbers, the aim of this paper is to extend certain Markov inequalities for the determinant of Hankel matrices and the zeros of the corresponding orthogonal polynomials on the real line…
We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimensional Heisenberg group. This is a particular case of a more…