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Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that…
Bounded cohomology of groups was first studied by Gromov in 1982. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic…
The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…
We study functions of bounded variation (and sets of finite perimeter) on a convex open set $\Omega\subseteq X$, $X$ being an infinite dimensional real Hilbert space. We relate the total variation of such functions, defined through an…
In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various…
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give…
Assuming that $S$ is the space of functions of regular variation, $\omega\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(\omega)$ if $$\|f\|^p_{B_p(\omega )}=\int_{B^n}…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those which hold in Euclidean spaces, in terms of the short-time behaviour of the heat…
We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
Given a convex set $C$ in a real vector space $E$ and two points $x,y\in C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:C\longrightarrow [m,M]$ is a bounded convex function. We then rewrite the…
The concept of contra function was introduced by Dontchev [2], in this work, we use the notion of T*12-open to study a new class of function called a contra-T*12-continuous function as a generalization of contra-continuous.
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
We compare possibilities of extension of bounded and unbounded Baire-one functions from subspaces of topological spaces.
In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…