Related papers: On the analytic functions

The aim of this study is to understand to what extent a 1-convex domain with Levi-flat boundary is capable of holomorphic functions with slow growth. This paper discusses a typical example of such domain, the space of all the geodesic…

In this paper, we study the near-boundary behavior of functions $u\in\mathcal{F}(\Omega)$ in the case where $\Omega$ is strictly pseudoconvex. We also introduce a sufficient condition for belonging to $\mathcal{F}$ in the case where…

If $f$ is in the Eremenko-Lyubich class (transcendental entire functions with bounded singular set) then $\Omega= \{ z: |f(z)| > R\}$ and $f|_\Omega$ must satisfy certain simple topological conditions when $R$ is sufficiently large. A model…

Let $U$ be a bounded open subset of the complex plane. Let $0<\alpha<1$ and let $A_{\alpha}(U)$ denote the space of functions that satisfy a Lipschitz condition with exponent $\alpha$ on the complex plane, are analytic on $U$ and are such…

Let $\Omega \subset \mathbb{R}^{n+1}$, $n \geq 1$, be an open and connected set. Set $\mathcal{T}_n$ to be the set of points $\xi \in \partial \Omega$ so that there exists an approximate tangent $n$-plane for $\partial\Omega$ at $\xi$ and…

Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…

An algebra $\mathcal{A}$ of real or complex valued functions defined on a set $\mathbf{T}$ shall be called \textit{homotonic} if $\mathcal{A}$ is closed under forming of absolute values, and for all $f$ and $g$ in $\mathcal{A}$, the product…

In this paper we study the geometry and the topology of unbounded domains in the Hyperbolic Space $\mathbb{H} ^n$ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic…

In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First we show that for a $C^1$-smooth totally geodesic Kobayashi isometric embedding $f\colon \Omega\to\Omega'$…

Let $n\in \mathbb N\cap[2,\infty)$. In this article, we show that there exists a bounded $C^1$ domain $\Omega\subset \mathbb R^n$ such that, for any given $s\in(1,2)\setminus\{\frac32\}$, \begin{align*} \left[H_0^1(\Omega),H^2(\Omega)\cap…

We show that the operations addition and multiplication on the set $C(\Omega)$ of all real continuous functions on $\Omega\subseteq\mathbb{R}^n$ can be extended to the set $\mathbb{H}(\Omega)$ of all Hausdorff continuous interval functions…

Let $\Omega$ be a bounded, weakly pseudoconvex domain in C^n, n > 1, with real-analytic boundary. A real-analytic submanifold $M \subset bd\Omega$ is called an analytic interpolation manifold if every real-analytic function on M extends to…

We find necessary and sufficient conditions on the function $\Phi$ for the inequality $$\Big|\int_\Omega \Phi(K*f)\Big|\lesssim \|f\|_{L_1(\mathbb{R}^d)}^p$$ to be true. Here $K$ is a positively homogeneous of order $\alpha - d$, possibly…

We consider convergence sets of formal power series of the form $f(z,t)=\sum_{n=0}^{\infty} f_n(z)t^n$, where $f_n(z)$ are holomorphic functions on a domain $\Omega$ in $\mathbb{C}$. A subset $E$ of $\Omega$ is said to be a convergence set…

We investigate the boundary behavior of holomorphic functions with respect to a family of curves in a domain of finite type. This work is a generalization of \u{C}irka's classical result on the unit ball and it supplements the result by…

We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on a closed oriented surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function,…

We give un upper bound Ent(\Omega, g)<\lambda\ of the diastatic entropy Ent(\Omega, g) of a complex bounded domain (\Omega, g) in terms of the balanced condition (in Donaldson terminology) of the Kaehler metric \lambda g. When (\Omega, g)…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^N$. Given a continuous plurisubharmonic function $u$ on $\Omega$, we construct a sequence of Gaussian analytic functions $f_n$ on $\Omega$ associated with $u$ such that…

Let $f$ be a zero-free analytic function on $\Re(s) \geq 1$. We prove that there exists an entire zero-free function $g$ and a Helson zeta-function $\zeta_\chi(s)=\sum_{n=1}^\infty \chi(n) n^{-s}$, where $\chi(n)$ is a completely…

Let $f:M\to \mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a connected component of some critical level of $f$, and $\mathcal{E}_V$ be its atom. Let also $\mathcal{S}(f)$ be a stabilizer of the function $f$ under the…