Related papers: Multivariable generalizations of the Schur class: …

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on…

A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function $n$ with a suitable…

We give a simplified exposition of Kummert's approach to proving that every matrix-valued rational inner function in two variables has a minimal unitary transfer function realization. A slight modification of the approach extends to…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

In this paper we establish a multivariable non-commutative generalization of L\"owner's classical theorem from 1934 characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex…

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…

We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…

We prove that graded $k$-Schur functions are $G$-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We expose a new miraculous shift invariance property of the graded $k$-Schur…

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 introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…

In this paper we shall use realization theory to prove new results about a class of holomorphic functions on an annulus \[R_\delta \stackrel{\rm def}{=} \{z \in \mathbb{C}: \delta <|z|<1\},\] where $0<\delta<1$. The class of functions in…

In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the `noncommutative Shilov boundary', and more particularly via the left multiplier operator algebra…

We prove the equivalence of a class of generalised Schur partition functions $\mathcal Z_G(q;\alpha)$ of 4d $\mathcal N=2$ superconformal gauge theories to contour integral representations of vector-valued modular forms of the type that…

For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| \leq A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The…

The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\lambda) = \exp(i(\lambda_1\psi_1 + ... + \lambda_n\psi_n)) for \lambda in R^n, gives rise to a manifold M of orthogonal projections…

We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with…

The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are…

Motivated by the canonical decomposition of contractions on Hilbert spaces, we investigate when contractive Toeplitz operators on vector-valued Hardy spaces on the unit disc admit a non-zero reducing subspace on which its restriction is…