Related papers: Caratheodory convergence and harmonic measure
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the…
We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
The purpose of this paper is to study convergence of Monge-Ampere measures associated to sequences of plurisubharmonic functions defined on a hyperconvex subset of ${\mathbb C^n}$.
We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We expand the classical balayage of measures and subharmonic functions on a system of rays $S$ with a common origin on the complex plane $\mathbb C$. This allows for an arbitrary subharmonic function $v$ of finite order on $\mathbb C$ build…
We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague convergence from the…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained…
Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept…
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences $(a_{n_1...n_d})_{n_1,...,n_d\in\bb N}$ such that for all orthonormal…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…