Related papers: Interpolation in the Nevanlinna class and harmonic…
We study two problems concerning harmonic measure on "champagne subdomains" of the unit disk. These domains are obtained by removing from the unit disk little disks around sequences of points with a uniform distribution with respect to the…
A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.
Three boundary Nevanlinna-Pick interpolation problems at finitely many points are formulated for generalized Schur functions. For each problem, the set of all solutions is parametrized in terms of a linear fractional transformation with a…
In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(\Delta-z)^{-1}, z\in\C\setminus\R^{+},$ has a meromorphic continuation through $\R^{+}$. The poles of this continuation are called resonances. When…
This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…
Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces of harmonic functions in the unit disk and multi-dimensional unit ball which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling…
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…
Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna…
We introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective…
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two…
The Lyapunov order appeared in the study of Nevanlinna-Pick interpolation for positive real odd functions with general (real) matrix points. For real or complex matrices $A$ and $B$ it is said that $B$ Lyapunov dominates $A$ if…
We study the scattering resonances arising from multiple $h$-dependent Dirac delta functions on the real line in the semiclassical regime $h \rightarrow 0$. We focus on resonances lying in strings along curves of the form $\text{Im } z \sim…
I describe a verifiable criterion for the solvability of the 2 by 2 spectral Nevanlinna-Pick problem with two interpolation points, and likewise for three other special cases of the mu-synthesis problem. The problem is to construct an…
In this paper we study the Nevanlinna-Pick matrix interpolation problem in the Carath\'eodory class with infinite data (both in the nondegenerate and degenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operator approach to…
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant…
Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every nonnegative function. In particular, this composition is the identity transform on the class of nonnegative…
We study harmonic functions which admit a certain majorant in the unit ball in $\R^m $. We prove that when the majorant fulfills a doubling condition, the extremal growth or decay may occur only along small sets of radii, and we give…
In this article we consider the class $\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc $\ID$ having a simple pole at $z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1 $. First we prove some sufficient…