Related papers: Commuting row contractions with polynomial charact…
To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic…
A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…
Representation theory of the symmetric group $\mathfrak{S}_n$ has a very distinctive combinatorial flavor. The conjugacy classes as well as the irreducible characters are indexed by integer partitions $\lambda \vdash n$. We introduce class…
To each finite-dimensional operator space $E$ is associated a commutative operator algebra $UC(E)$, so that $E$ embeds completely isometrically in $UC(E)$ and any completely contractive map from $E$ to bounded operators on Hilbert space…
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…
The purpose of the paper is to obtain estimates for differences of functions of two pairs of commuting contractions on Hilbert space. In particular, Lipschitz type estimates, H\"older type estimates, Schatten--von Neumann estimates are…
Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
We introduce the notion of $k$-regular factorizations for contractions into $k$ factors, generalizing the classical notion of regular factorization due to Sz.-Nagy and Foia\c{s}, and develop a systematic framework for their analysis. Using…
We investigate determinants of Koszul complexes of holomorphic functions of a commuting tuple of bounded operators acting on a Hilbert space. Our main result shows that the analytic joint torsion, which compares two such determinants, can…
The main result of this note is a characterization of the Poisson commutativity of Hamilton functions in terms of their principal action functions.
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
We extend the de Branges-Rovnyak model for completely non-coisometric (CNC) linear contractions on a Hilbert space to the non-commutative multivariate setting of CNC row contractions. Namely, we show that any CNC contraction from several…
A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is…
We give a recursive definition of generalized parking function that allows us to view them as a species. From there we compute a non-commutative characteristic of the generalized parking function module, and deduce some enumeration formulas…