Related papers: A determinant formula for Toeplitz operators assoc…
A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute…
This paper presents sharp estimates for the second-order Toeplitz determinant whose entries are the coefficients of convex functions defined on the unit disk in $\mathbb{C}$. These estimates are further extended to a subclass of holomorphic…
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
The theory of Toeplitz quantization presented in our previous paper is extended and further developed to include diverse and interesting non-commutative realizations of the classical Euclidean plane. This is done using Hilbert spaces of…
In a previous paper [KT] we introduced determinant of the Riemann operator on Quillen's higher $K$-groups of the integer ring of an algebraic number field $K$. We showed that the determinant expresses essentially the inverse of the so…
Sharp upper and lower bounds for the second and third order Hermitian-Toepilitz determinants are obtained for some generalized subclasses of starlike and convex functions. Applications of these results are also discussed for several widely…
This paper deals with bracket flows of Hilbert-Schmidt operators. We establish elementary convergence results for such flows and discuss some of their consequences.
Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the…
In this note we describe the commutant of the multiplication operator by a monomial in the Toeplitz algebra of a complete strongly pseudoconvex Reinhardt domain.
Given a polyanalytic function, we show that the corresponding Toeplitz operator on the Bergman space of the unit disc can be expressed as a quotient of certain differential operators with holomorphic coefficients. This enables us to obtain…
In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining…
The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded…
A certain determinant is evaluated by guessing and computing the LU-decomposition.
Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $SU_q(2)$ is such…
We bring together two apparently disconnected lines of research (of mathematical and of physical nature, respectively) which aim at the definition, through the corresponding zeta function, of the determinant of a differential operator…
We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$…
We make a progress towards describing the commutants of Toeplitz operators with harmonic symbols on the Bergman space over the unit disk. Our work greatly generalizes several partial results in the field.
We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the $H^2$ and $H^{\infty}$ norms of functions in model spaces.
We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise…
In this paper, we establish the sharp bounds of certain Toeplitz determinants formed over the coefficients of mappings from a class defined on the unit ball of complex Banach space and on the unit polydisc in $\mathbb{C}^n$. Derived bounds…