Related papers: Factorizations of Schur functions
In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined a Banach algebra E…
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…
We classify and construct all multiplicity-free plethystic products of Schur functions. We also compute many new (infinite) families of plethysm coefficients, with particular emphasis on those near maximal in the dominance ordering and…
For a simple Lie algebra $\mathfrak{g}$ and an irreducible faithful representation $\pi$ of $\mathfrak{g}$, we introduce the Schur polynomials of $(\mathfrak{g},\pi)$-type. We then derive the Sato-Zhou type formula for tau functions of the…
Every function in the Dirichlet space on the unit disc has an inner/outer factorization. We study which inner functions occur in this way. For Blaschke products, this is the well known question of which subsets of the disc are zero sets for…
In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new class…
In this paper we study a class $\mathcal R\mathcal S(\mathfrak M)$ of operator functions that are holomorphic in the domain $\mathbb C\setminus\{(-\infty,-1]\cup [1,+\infty)\}$ and whose values are contractive operators in a Hilbert space…
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
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…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…
Harmonic and polyanalytic functional calculi have been recently defined for bounded commuting operators. Their definitions are based on the Cauchy formula of slice hyperholomorphic functions and on the factorization of the Laplace operator…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
An explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained that makes Schwarzian functional integrals calculus simpler and more transparent.
We study the asymptotics of Schur polynomials with partitions $\lambda$ which are almost staircase; more precisely, partitions that differ from $((m-1)(N-1),(m-1)(N-2),\ldots,(m-1),0)$ by at most one component at the beginning as…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…
An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers $S$ for the reproducing kernel Hilbert space ${\mathcal H}(k_{d})$ on the unit ball ${\mathbb…
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…
The Fueter mapping theorem gives a constructive way to extend holomorphic functions of one complex variable to monogenic functions, i.e., null solutions of the generalized Cauchy-Riemann operator in $\mathbb{R}^4$, denoted by $\mathcal{D}$.…
Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and…
We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion…