Related papers: Polynomial local functionals on convex functions

We prove a version of both Jacobi's and Montel's Theorems for the case of continuous functions defined over the field $\mathbb{Q}_p$ of $p$-adic numbers. In particular, we prove that, if \[ \Delta_{h_0}^{m+1}f(x)=0 \ \ \text{for all}…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

Two classes of measure-valued valuations on convex functions related to Monge-Amp\`ere operators are investigated and classified. It is shown that the space of all valuations with values in the space of complex Radon measures on…

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…

We conclude the classification of spaces of continuous functions on ordinals carried out by R. Gorak. This gives a complete topological classification of the spaces $C_p([0,\alpha])$ of all continuous real-valued functions on compact…

We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…

We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…

All non-negative, continuous, $\operatorname{SL}(n)$ and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^n$ are classified. Furthermore, using the invariance of the function space under the…

We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also…

We generalize the phenomenon of continuation from complex anal- ysis to locally operator monotone functions. Along the lines of the egde-of- the-wedge theorem, we prove continuations exist dependent only on geometric features of the domain…

We study the relation of $L$-equivalence, which derives from the construction of the free locally convex spaces, through a concept that particularizes several notions related to the simultaneous extension of continuous functions. We also…

We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a differential operator of infinite order D(C)…