Related papers: Quasi-linear functionals on locally compact spaces

Let $X$ be a normed space of a finite dimension at least two, and $C\subsetneq X$ a closed convex set with nonempty interior. We are interested in extending Lipschitz quasiconvex functions on $C$ to quasiconvex functions on $X$. We show…

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such…

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with 1<p<\infty, and connect them to the Sobolev theory in R^n. In…

We introduce the strong Gelfand-Phillips property for locally convex spaces and give several characterizations of this property. We characterize the strong Gelfand-Phillips property among locally convex spaces admitting a stronger Banach…

We analyze the relationship between Borel measures and continuous linear functionals on the space $\mathrm{Lip}_0(M)$ of Lipschitz functions on a complete metric space $M$. In particular, we describe continuous functionals arising from…

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups…

Recently the first author studied the bifurcation of critical points of families of functionals on a Hilbert space, which are parametrised by a compact and orientable manifold having a non-vanishing first integral cohomology group. We…

In this paper we investigate the nature of stationary points of functionals on the space of Riemannian metrics on a smooth compact manifold. Special cases are spectral invariants associated with Laplace or Dirac operators such as functional…

We introduce and study a new class of generalized convex functions termed star quasiconvex functions. This class includes convex, star-convex, quasiconvex, quasar-convex, and positively homogeneous functions of any degree $p>0$ as special…

Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not necessarily bounded from above) $m-$subharmonic function $D$ by continuous $m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also consider the…

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces…

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…

Let $E$ be a real vector space with dual space $E^*$ and let $C\subset E$ be a convex subset with more than one point. Let $f : C\to\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary…

We prove that certain nonlocal functionals defined on partitions made of measurable sets Gamma-converge to a local functional modeled on the perimeter in the sense of De Giorgi. Those nonlocal functionals involve generalized surface tension…

We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…

We define a new gauge independent quasi-local mass and energy, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed…

We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…