Related papers: Vitushkin-type theorems
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
We prove a long-standing conjecture of Chudnovsky for very general and generic points in $\mathbb{P}_k^N$, where $k$ is an algebraically closed field of characteristic zero, and for any finite set of points lying on a quadric, without any…
The main goal of the paper is to present a general model theoretic framework to understand a result of Shalev on probabilistically finite nilpotent groups. We prove that a suitable group where the equation $[x_1,\ldots,x_k]=1$ holds on a…
The Eremenko-Lyubich class consists of transcendental entire functions with bounded singular set and the Speiser class is made up of functions with a finite singular set. In an earlier paper "Models for the Eremenko-Lyubich class" I gave a…
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an…
We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged…
In this paper we prove global existence of classical solutions to the Vlasov-Poisson and the ionic Vlasov-Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms $G_p: T_pM \to [0,\infty]$ are given. When we consider sub-Riemannian manifolds, our definition coincide with…
This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L^p-functions, by means of positive linear…
In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve the constant functions involving non-negative parameter ?. We derive the approximation behaviour of these operators including global…
Let $f:\mathbb{R}^n\to\mathbb{R}$ be a function. Assume that for a measurable set $\Omega$ and almost every $x\in\Omega$ there exists a vector $\xi_x\in\mathbb{R}^n$ such that $$\liminf_{h\to 0}\frac{f(x+h)-f(x)-\langle \xi_x,…
We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on…
In this paper, we obtained some global approximation results for general Gamma type operators.
If $f$ is in the Eremenko-Lyubich class (transcendental entire functions with bounded singular set) then $\Omega= \{ z: |f(z)| > R\}$ and $f|_\Omega$ must satisfy certain simple topological conditions when $R$ is sufficiently large. A model…
Let $F$ be a non-archimedean local field, let $k$ be an algebraically closed field of characteristic $\ell$ different from the residual characteristic of $F$, and let $A$ be a commutative Noetherian $W(k)$-algebra, where $W(k)$ denotes the…
We prove the following result due to Hamidoune using an analytic approach. Suppose that A is a subset of a finite group G with |AA^{-1}| \leq (2-\varepsilon)|A|. Then there is a subgroup H of G and a set X of size O_\varepsilon(1) such that…
We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of…
One important class of tools in the study of the connections between algebraic and topological structures are the "Banach-Stone type theorems", which describe algebraic isomorphisms of algebras (or groups, lattices, etc.) of functions in…
We give a parametrization with perfect sets of the abstract Ellentuck theorem. The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known…