Related papers: Value distribution and linear operators
The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for…
We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions…
We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…
We construct a generalization of the multiplicative product of distributions presented by L. H\"ormander in [L. H\"ormander, {\it The analysis of linear partial differential operators I} (Springer-Verlag, 1983)]. The new product is defined…
The $\varphi$-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex…
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
Some differential implications of classical Marx-Strohh\"acker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential…
The meromorphic solutions $f$ with $\rho_2(f)<1$ of the non-linear difference equation \begin{align*} f^n(z)+P_d(z,f)=p_1e^{{\lambda_1}z}+p_2e^{{\lambda_2}z}+p_3e^{{\lambda_3}z}, \end{align*} are characterized in terms of exponential…
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we…
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…
We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. The construction covers cases where non-integer powers of $z$ and also terms containing…
In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…
In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such…
The subject of our thesis is the uniqueness theory of meromorphic functions and it is devoted to problems concerning Bruck conjecture, set sharing and related topics. The tool, we used in our discussions is classical Nevanlinna theory of…
A complex function $f(z)$ is called a Herglotz-Nevanlinna function if it is holomorphic in the upper half-plane ${\mathbb C}_+$ and maps ${\mathbb C}_+$ into itself. By a maximum principle a Herglotz-Nevanlinna function which takes a real…
Let $\mathbb{D}$ be a division ring and $\mathbb{F}$ be a subfield of the center of $\mathbb{D}$ over which $\mathbb{D}$ has finite dimension $d$. Let $n,p,r$ be positive integers and $\mathcal{V}$ be an affine subspace of the…
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes,…
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…
It is proved that for any positive number $\lambda$, $1<\lambda<2$; there exists a meromorphic function $f$ with logarithmic order $\lambda$= $\displaystyle\limsup_{r\to+\infty}\frac{\log T(r,f)}{\log\log r}$ such that $f$ has no Julia…
We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the density functions of such value-distributions for any…