复变函数
Loewner chains are ubiquitous in the theory of slit mappings, and hence in the study of bounded conformal maps. They have attracted new interest in the past decades through their applications to statistical physics and fractal geometry,…
A pole of order $m \in \mathbb{N}$ at $\beta \in \mathbb{C}$ of a regular operator valued function $Q : \mathcal{D}(Q) \to \mathcal{L}(\mathcal{H})$ is investigated. We provide a characterization of pole cancellation functions…
We prove isoperimetric-type inequalities for pluriharmonic functions in the unit polydisc $\mathbb{U}^n$. Let $h^p(\mathbb{U}^n)$ and $b^p_{\mathbf{q}}(\mathbb{U}^n)$ denote, respectively, the pluriharmonic Hardy space and the pluriharmonic…
In this paper, we prove that local polynomial convexity at the origin for the union of finitely many transverse totally real subspaces of maximal dimension is sufficient for Carleman approximation. Some new conditions are given for the…
The vector calculus in non-integer dimensional space (NIDS), including the NIDS version of the standard vector differential operators (gradient, divergence, and curl) is well-known. A deformation of the quaternionic Moisil-Teodorescu…
In this paper, we study two problems concerning holomorphic flows on $\mathbb C^n$. First, we prove Runge-type results for positive-time flow invariant domains. For a linear flow $e^{tA}$, where $A\in GL(n,\mathbb C)$, let $E^s$, $E^u$, and…
The classical Bohr inequality states that if $f(z)=\sum_{n=0}^{\infty} a_n z^n$ is analytic and $|f(z)|<1$ in the unit disk $\mathbb{D}$, then $\sum_{n=0}^{\infty} |a_n| r^n \le 1$ for $|z|=r \le 1/3$, where $1/3$ is sharp. Extending this…
Let $T$ be a positive $\ddc$-closed current of bidimension $(1,1)$ on a projective manifold $X$ of dimension $n.$ We show that for every $c > 0$ the set of points of $X$ where the Lelong number of $T$ is larger or equal to $c$ is an…
Motivated by recent developments in complex difference equations and Nevanlinna theory in several complex variables, we investigate finite-order transcendental entire solutions of the coupled Fermat-type difference system: \beas…
In this paper, we provide an integration by parts formula for plurisubharmonic functions on a hyperconvex domain that are bounded outside a compact set. This extends a previous result of Urban Cegrell.
Our main result is a characterization of $g$ for which the operator $S_g(f)(z) = \int_0^z f'(w)g(w)\, dw$ is bounded below on the Bloch space. We point out analogous results for the Hardy space $H^2$ and the Bergman spaces $A^p$ for $1 \leq…
We normalize a first-order real planar elliptic system, by pointwise algebra, to a framed Beltrami-Vekua equation $\Phi(w_{\bar z} - \mu w_z) + \Psi(\overline{w_z} - \mu\,\overline{w_{\bar z}}) + \mathfrak{a} w + \mathfrak{b} \bar w =…
This paper investigates the analytic structure of the parametric harmonic zeta function \[ \zeta_{H}\left( s,a,b\right) =\sum_{n=0}^{\infty}\frac{H_{n}\left( a\right) }{\left( n+b\right) ^{s}}, \] where $H_{n}\left( a\right) $ denotes the…
We construct examples of uniformly quasiregular mappings (uqr) acting on a sphere and having Fatou set consisting of infinitely many components. In particular we construct a uqr mapping providing a higher dimensional counterpart for the…
Let $\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\infty$, and let $\phi=b/a$, where $a$ is the Pythagorean mate of $b$. It is known that, if $f$ is a function holomorphic on a…
We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…
In this paper, we investigate two subclasses of analytic and univalent functions associated with the exponential mapping $\varphi(z)=e^{\alpha z},\qquad 0<\alpha\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec…
In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates…
Dobbs proved that the second iterate of almost every line in the complex plane under the exponential function is dense in the plane. In this paper, we prove an analogous result for the second iterate of the Zorich map in $\mathbb{R}^3$.
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.