Related papers: On extension functions for image space with differ…
When dealing with certain mathematical problems, it is sometimes necessary to show that some function induces a metric on a certain space. When this function is not a well renowned example of a distance, one has to develop very particular…
We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of…
We provide necessary and sufficient conditions for a tempered distribution $F\in S'(R)$ to be positive definite. A generalized Cauchy transform $\widetilde{F}$ of $F$ is used as a numerical continuation of $F$ to the open upper and lower…
We establish sufficient conditions for extension of weighted square integrable holomorphic functions from a possibly singular hypersurface to the ambient affine space. The norms we use are the so-called Bargmann-Fock norms, and thus there…
We give necessary and sufficient conditions on a function $f:[0,1]\to {0,1,2,...,\omega,\continuum}$ under which there exists a continuous function $F:[0,1]\to [0,1]$ such that for every $y\in[0,1]$ we have $|F^{-1}(y)|=f(y)$.
In a previous paper, we studied certain sequences of simultaneous rational approximations in ${\bf R}^2$ which present some analogy with the continued fractions. We got results around the Littlewood conjecture by using such approximations.…
We study functionals on the space of almost complex structures on a compact $\mathbb{C}$-manifold, whose variational properties could be used to tackle Yau's Challenge.
In this paper we discuss the existence of solutions to vectorial differential inclusions. We investigate sufficient conditions for existence, more flexible than those available in the literature, so that important applications can be fitted…
For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
We discuss a general result of holomorphic extension of a real analytic function $f$ defined on the boundary $\partial D$ of a real analytic strictly convex subset $D\subset\subset \C^n$. We show that this follows from the hypothesis of…
In this note we give a simple sufficient condition for an affine iterated function system to admit an invariant affine subspace persistently with respect to changes in the translation parameters. This yields further examples of tuples of…
We show that the existing generalized separation statements including the conventional extremal principle and its extensions differ {in the ways norms on product spaces are defined}. We prove a general separation statement with arbitrary…
We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…
We show that, under certain regularity assumptions, there exists a linear extension operator.
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
We obtained some upper bounds for the pseudocharacter of the space C(X,Y) at a point f.
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.