Related papers: Asymmetric variations of multifunctions with appli…
We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet…
We prove a Lusin approximation of functions of bounded variation. If $f$ is a function of bounded variation on an open set $\Omega\subset X$, where $X=(X,d,\mu)$ is a given complete doubling metric measure space supporting a $1$-Poincar\'e…
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
We investigate the invariant metrics and complex geodesics in the universal Teichm\"{u}ller space and Teichm\"{u}ller space of the punctured disk using Milin's coefficient inequalities. This technique allows us to establish that all…
We obtain sharp estimates of the Hardy-Vitali type total $p$-variation of a function of two variables in terms of its mixed modulus of continuity in $L^p([0,1]^2)$. We also investigate various embeddings for mixed norm spaces of bivariate…
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…
The existence of continuous not necessarily bounded solutions of nonlinear functional Volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity. New abstract topological fixed…
For $f_1,...,f_r\in \mathbb C[z_1,...,z_n]\setminus \mathbb C$, we introduce the variation of archimedean zeta function. As an application, we show that the $n/d$-conjecture, proposed by Budur, Musta\c{t}\u{a}, and Teitler, holds for…
Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…
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 give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
We determine, up to exponentiating, the polar locus of the multivariable archimedean zeta function associated to a finite collection of polynomials F. The result is the monodromy support locus of F, a topological invariant. We give a…
We establish in this paper, an existence and uniqueness result of right continuous with bounded variation solution for a perturbed differential inclusion governed by time-dependent maximal monotone operators.
In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous…
Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a nondecreasing sequence of pseudometrics $\{\nu_n\}$ on $M^T$ (the set of all functions from $T$ into $M$), called the \emph{joint modulus of variation}. We prove that if two…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We analyze the boundaries of multiply connected Fatou components of transcendental maps by means of universal covering maps and associated inner functions. A unified approach is presented, which includes invariant Fatou components (of any…
In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that the total variation of functions of bounded variation is lower semicontinuous with respect to $L^1$-convergence in…
We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…