Related papers: Common boundary values of holomorphic functions fo…

A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…

We show that, if $f$ is an outer function and $a\in[0,1)$, then the set of functions $\{\log |(f\circ\psi)^*|: \psi:\mathcal{D}\to\mathcal{D} \text{ holomorphic}, |\psi(0)|\le a\}$ is uniformly integrable on the unit circle. As an…

In this paper, we establish strong holomorphic Morse inequalities on non-compact manifolds under the condition of optimal fundamental estimates. We show that optimal fundamental estimates are satisfied and then strong holomorphic Morse…

It was recently shown that under mild assumptions second-order conformally superintegrable systems can be encoded in a $(0,3)$-tensor, called structure tensor. For abundant systems, this approach led to algebraic integrability conditions…

We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into $\C\P^2$. The formula may be considered as an analogue of the Green's formula for domains in $\C$.

A Morse 2-function is a generic smooth map from a smooth manifold to a surface. In the absence of definite folds (in which case we say that the Morse 2-function is indefinite), these are natural generalizations of broken (Lefschetz)…

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

In this paper we prove that every smooth complete closed complex hypersurface in the open unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ $(n\ge 2)$ is a level set of a noncritical holomorphic function on $\mathbb{B}_n$ all of whose level sets…

Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A…

Let $M$ be a 2-disk or a cylinder, and $f$ be a smooth function on $M$ with constant values at $\partial M$, devoid of critical points in $\partial M$, and exhibiting a property wherein for every critical point $z$ of $f$ there is a local…

In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\norm{f(z_1,z_2)}\leq K(\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\CC[[z_1,z_2]]$, and $K$ is…

Let $f\in W^{3,1}_{\mathrm{loc}}(\Omega)$ be a function defined on a connected open subset $\Omega\subseteq\mathbb R^2$. We will show that its graph is contained in a quadratic surface if and only if $f$ is a weak solution to a certain…

The notion of a quasi-free Hilbert module over a function algebra $\mathcal{A}$ consisting of holomorphic functions on a bounded domain $\Omega$ in complex $m$ space is introduced. It is shown that quasi-free Hilbert modules correspond to…

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…

Let $\Omega_1$, $\Omega_2$ be two domains in $\mathbb{C}^n$ with Kobayashi metrics $k_{\Omega_i}$ and consider $f \in \mathcal{O}(\Omega_1,\Omega_2)$ a holomorphic mapping. Let $\mathfrak{F}_1$ and $\mathfrak{F}_2$ be a family of geodesics…

We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…

We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…

In this paper we prove the result: Let $\mathcal{F}$ be a family of meromorphic functions on a domain $\Omega$ such that every pair of members of $\mathcal{F}$ shares a set $S:=\left\{\psi_1(z), \psi_2(z), \psi_3(z) \right\}$ in $\Omega$,…

Let M be a closed (n-1)-connected 2n-dimensional smooth manifold with n > 2. In terms of the system of invariants for such manifolds introduced by Wall, we obtain necessary and sufficient conditions for M to admit an almost complex…

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…