Related papers: On the Nevanlinna problem - Characterization of al…

Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}$ of the form $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ and $\mathcal{S}$ denote the class of functions $f\in\mathcal{A}$ which are univalent ({\it i.e.},…

Denote by $\mathcal{P}_{\log}$ the set of all non-constant Pick functions $f$ whose logarithmic derivatives $f^{\, \prime}/f$ also belong to the Pick class. Let $\mathcal{U}(\Lambda)$ be the family of functions $z\cdot f(z)$, where $f…

We characterize the zero sets of functions in the Schur--Agler class over the unit polydisk as well as functions in the unit ball of the multiplier algebra of the Drury--Arveson space via operators associated with a unitary realization…

Let $A$ be a square complex matrix, $z_1$, ..., $z_{n}\in\mathbb C$ be (possibly repetitive) points of interpolation, $f$ be analytic in a neighborhood of the convex hull of the union of the spectrum of $A$ and the points $z_1$, ...,…

We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class…

General results of interpolation (eg. Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebra $F^\infty$ (resp. noncommutative disc algebra $A_n$) with consequences to the interpolation by bounded operator-valued…

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…

The tetrablock is the set $$ \mathcal{E}=\{x \in \mathbb{C}^3: \quad 1-x_1z-x_2w+x_3z w \neq 0 \quad whenever \quad |z|\leq 1, |w|\leq 1\}. $$ The closure of $\mathcal{E}$ is denoted by $\overline{\mathcal{E}}$. A tetra-inner function is an…

We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…

We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…

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…

Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so…

Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k,n\in\mathbb{N}$ and let \begin{align*} \Omega_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\;…

Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a…

We show that the derivative f' of the generic function f in the disk algebra lies outside of the localized Nevanlinna class for every arc in the unit circle.

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their…

We prove a Bernstein-type inequality involving the Bergman and the Hardy norms, for rational functions in the unit disc \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D}, 0

We prove that, given a function $f$ in the Nevanlinna class $N$ and a positive integer $n$, there exist $g\in N$ and $h\in BMOA$ such that $f^{(n)}=gh^{(n)}$. We may choose $g$ to be zero-free, so it follows that the zero sets for the class…

We introduce Nevanlinna--Pick norms associated with finite families of characters in a commutative semisimple Banach algebra and study the class $NP_\infty$, where all such norms are minimal. Our main result is a topological rigidity…

An indefinite variant of the abstract interpolation problem is considered. Associated to this problem is a model Pontryagin space isometric operator V. All the solutions of the problem are shown to be in a one-to-one correspondence with a…