Related papers: On the nature of Bregman functions
Given a continuous function $\phi$ defined on a domain $\Omega\subset\mathbb{R}^m\times\mathbb{R}^n$, we show that if a Pr\'ekopa-type result holds for $\phi+\psi$ for any non-negative convex function $\psi$ on $\Omega$, then $\phi$ must be…
We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, to be polynomially convex. Almost all sufficient conditions known to date --- provided the function…
Given an unbounded strongly pseudoconvex domain D and a continuous real valued function h defined on bD, we study the existence of a (maximal) plurisubharmonic function u on D such that u=h on bD.
If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is…
Liebmann's Theorem asserts that a compact, connected, convex surface with constant mean curvature (CMC) in the Euclidean space must be a totally umbilical sphere. In this article we extend Liebmann's result to hypersurfaces with boundary.…
A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb…
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…
We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…
In this paper, we study the properties of integral functionals induced on $L^1_E (S,\mu)$ by closed convex functions on a Euclidean space $E$. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We…
In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…
We prove that if $D\subset C^n$ is a bounded domain with real analytic boundary and D is pseudoconvex then the compact open topology in the group of holomorphic automorphisms of D is the topology of uniform convergence on D.
Given a function $f$ defined on a nonempty and convex subset of the $d$-dimensional Euclidean space, we prove that if $f$ is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
In this paper, we prove that every continuous $h$-mid-convex with suitable conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem, Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.
Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial…
A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of…
The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…
The notion of Bregman divergence and sufficiency will be defined on general convex state spaces. It is demonstrated that only spectral sets can have a Bregman divergence that satisfies a sufficiency condition. Positive elements with trace 1…
A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in…
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…