Related papers: Value distribution and linear operators
In this note we compare two recent results about the distribution of eigenvalues for semi-classical pseudodifferential operators in two dimensions. For classes of analytic operators A. Melin and the author obtained a complex Bohr-Sommerfeld…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
We give an introduction to the valuation theoretical phenomenon of "defect", also known as "ramification deficiency". We describe the role it plays in deep open problems in positive characteristic: local uniformization (the local form of…
The following version of the Lumer-Phillips is proved: a surjective dissipative operator is m-dissipative and invertible. The result remains true if dissipative linear relations (i.e multivalued operators) are considered. The main purpose…
In the present paper, we show that, for every $\delta>0$, the function $(\log {\mathcal{L}}(s))^{(m)}$, where $m\in {\mathbb{N}} \cup \{ 0\}$ and ${\mathcal{L}} (s) := \sum_{n=1}^\infty a(n) n^{-s}$ is an element of the Selberg class…
The model of kappa-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper we present new results concerning different sets of derivatives on the coordinate algebra of…
We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…
Favard's theorem characterizes bases of functions $\{p_n\}_{n\in\mathbb{Z}_+}$ for which $x p_n(x)$ is a linear combination of $p_{n-1}(x)$, $p_n(x)$, and $p_{n+1}(x)$ for all $n \geq 0$ with $p_{0}\equiv1$ (and $p_{-1}\equiv 0$ by…
We generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize the classical mean value…
Given an entire function $f$ of finite order $\rho$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{\lambda+\varepsilon})+S(r,f)$,…
In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operator and the final term is the Kipriyanov operator of…
The classic Schneider-Lang theorem in transcendence theory asserts that there are only finitely many points at which algebraically independent complex meromorphic functions of finite order of growth can simultaneously take values in a…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both…
In this paper, we introduce certain $n$-th order nonlinear Loewy factorizable algebraic ordinary differential equations for the first time and study the growth of their meromorphic solutions in terms of the Nevanlinna characteristic…
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We prove a general version of the "Stability Theorem": if $K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $F|K$ is a finitely generated (transcendental) extension of…
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.