Related papers: Inverse mean value properties (a survey)
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
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…
Asymptotic mean value properties, their converse and some other related results are considered for solutions to the $m$-dimensional Helmholtz equation (metaharmonic functions) and solutions to its modified counterpart (panharmonic…
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic…
The paper deals with some elementary problems about various mean value properties and their connections to harmonic functions and random walks.
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
The mean value inequality is characteristic for upper semicontinuous functions to be subharmonic. Quasinearly subharmonic functions generalize subharmonic functions. We find the necessary and sufficient conditions under which subsets of…
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.
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…
We investigate functions with the property that for every interval, the slope at the midpoint of the interval is the same as the average slope. More generally, we find functions whose average slopes over intervals are given by the slope at…
In this paper, some geometric properties of inverse polynomial images which consist of a real interval and an arc symmetric with respect to the real line are obtained. The proofs are based on properties of Jacobi's elliptic and theta…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
For functions defined on the $n$-dimensional hypercube $I_n (r) = \{{\bm{x}} \in \mathbb{R}^n ~\vert~ \vert x_i \vert \le r,~ i = 1, 2, \ldots , n\}$ and harmonic therein, we establish certain analogues of Gauss surface and volume…
In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…
We introduce and study strongly and weakly harmonic functions on metric measure spaces defined via the mean value property holding for all and, respectively, for some radii of balls at every point of the underlying domain. Among properties…