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We study functions of bounded variation defined in an abstract Wiener space X, relating the variation of a function u on a convex open set O in X to the behavior near t=0 of T(t)u, T(t) being the Ornstein--Uhlenbeck semigroup in O.
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We investigate several boundedness properties of function spaces considered as uniform spaces.
In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…
This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particular, the main result proves that the total variation of a…
Let $f\in L_{2\pi}$ be a real-valued even function with its Fourier series $ \frac{a_{0}}{2}+\sum_{n=1}^{\infty}a_{n}\cos nx,$ and let $S_{n}(f,x), n\geq 1,$ be the $n$-th partial sum of the Fourier series. It is well-known that if the…
We establish certain fine properties for functions of bounded $\mathscr A$-variation known in the classical $BV$ setting. Here, $\mathscr A$ is a $k$th order constant-coefficient homogeneous linear differential operator with a…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
In this paper, we define and study the space of all the functions of bounded variation $f:[x,y]\to \mathbb{Y}$ denoted by $\mathcal{BV}[x,y],$ where $[x,y]$ is an ordered interval and $\mathbb{Y}$ is an absolute order unit space having…
In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.