Related papers: Schur Class Operator Functions and Automorphisms o…

We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane (Schur/Herglotz functions over…

We construct the chiral algebra associated with the $A_{1}$-type class $\mathcal{S}$ theory for genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we…

The Virasoro operations in Witten's theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur's ring \Delta of…

For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Let $L=-\Delta +V$, $V\geq 0$, be the Dunkl--Schr\"odinger operator on $\mathbb R^N$. Assume that there…

SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition…

We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations…

In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces…

In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit…

Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and orientation $\Omega$. In previous work we associated an algebra $H$ to this data, such that the locally free $H$-modules behave in many aspects like…

Let $\mathcal{T}_{+}(E)$ be the tensor algebra of a $W^{*}$-correspondence $E$ over a $W^{*}$-algebra $M$. In earlier work, we showed that the completely contractive representations of $\mathcal{T}_{+}(E)$, whose restrictions to $M$ are…

A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

We consider the expansion of the square of a complete homogeneous function $h_\lambda$, or of an elementary symmetric function $e_\lambda$, in the basis of Schur functions. This square also decomposes into two plethysms, $s_2[h_\lambda]$…

Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by…

We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard…

In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to…

We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra of the symmetric functions $\Gamma$ generated by odd power sums. We give a graphical description of the factorial Schur $Q$-functions as…

We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the…

Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,z_2,\ldots, z_n\in \Omega$ and $w_1,w_2,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the \textit{Pick interpolation problem} asks when there…

We study reflexivity and structure properties of operator algebras generated by representations of the discrete Heisenberg semi-group. We show that the left regular representation of this semi-group gives rise to a semi-simple reflexive…