Related papers: On meromorphic functions defined by a differential…

It is proved that the group of holomorphic automorphisms of holomorphically homogeneous nondegenerate (finite Bloom-Graham type + holomorphic nondegenaracy) model surface Q is a subgroup of the group of birational automorphisms of the…

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…

Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where $\psi$ is a Bernstein function, $g$ is a bounded completely monotone function and $-A$ is the generator of a holomorphic $C_0$-semigroup on a Banach…

We extend the classical theorem of Uchiyama about constructive Fefferman-Stein decompositions of ${\rm BMO}$ functions by systems of singular integrals to the rational Dunkl setting. On $\mathbb{R}^N$ equipped with a root system $R$ and a…

We give a simple proof, with some complements, of a result of Cerveau and Lins Neto, concerning the existence of meromorphic first integrals for germs of codimension one foliations with an invariant real hypersurface.

In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number, and let $a,b,c\in\hat{S}(f)$ be…

Given $\u$ a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, $H_{b\u}(E)$. We prove that, under very natural conditions verified by many usual classes of…

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$--dimensional $K(G,1)$ and $H \leq G$ is of type $F_{n+1}$, then the $n^{th}$--homological filling…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real…

Let $X$ be an integral affine or projective hypersurface over a field $F$ of characteristic $p>0$, and let $F(X)$ denote its function field. In a recent article, Dolphin and Hoffmann obtained an explicit description of the kernel of the…

Germs of rational functions~$h$ on points $p$ of smooth varieties~$S$ define germs of rational maps to the projective line. Assume that $p$ is in the indeterminacy locus of $h$. If $\pi:\hat{S}\to S$ is a birational map which is an…

We show in this note that for a germ $g$ of holomorphic function with an isolated singularity at the origin of $\mathbb{C}^n$ there is a pole for the meromorphic extension of the distribution \begin{equation*} \frac{1}{\Gamma(\lambda)}…

We study the functional identity $G(x)f(x)=H(x)$ on a division ring $D$, where $f \colon D\to D$ is an additive map and $G(X)\ne 0, H(X)$ are generalized polynomials in the variable $X$ with coefficients in $D$. Precisely, it is proved that…

We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…

Let $X\subset Y(1)^n$ be a subvariety defined over a number field $\mathbb F$ and let $(P_1,\ldots,P_n)\in X$ be a special point not contained in a positive-dimensional special subvariety of $X$. We show that the if a coordinate $P_i$…

Let $M$\/ be a subharmonic function with Riesz measure $\mu_M$ on the unit disk $\mathbb D$ in the complex plane $\mathbb C$. Let $f$ be a nonzero holomorphic function on $\mathbb D$ such that $f$ vanishes on ${\sf Z}\subset \mathbb D$, and…

In this paper, a normality criterion concerning a sequence of meromorphic functions and their differential polynomials is obtained. Precisely, we have proved: Let $\left\{f_j\right\}$ be a sequence of meromorphic functions in the open unit…

Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic…

The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joint spectra have been stated, the condition for holomorphy of…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…