相关论文: Lower bounds for quasianalytic functions, II. The …

Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a…

Quasianalytic classes are classes of infinitely differentiable functions that satisfy the analytic continuation property enjoyed by analytic functions. Two general examples are quasianalytic Denjoy-Carleman classes (of origin in the…

This expository article is devoted to the notion of quasianalytic classes and the Borel mapping. Although quasianalytic classes are well known in analysis since several decades. We are interested in certain properties of Denjoy-Carleman's…

We prove two main results on Denjoy-Carleman classes: (1) a composite function theorem which asserts that a function f(x) in a quasianalytic Denjoy-Carleman class Q, which is formally composite with a generically submersive mapping y=h(x)…

Let $X$ be a perfect, compact subset of the complex plane. We consider algebras of those functions on $X$ which satisfy a generalised notion of differentiability, which we call $\mathcal{F}$-differentiability. In particular, we investigate…

A classical result of Carleman, based on the theory of quasianalytic functions, shows that polynomials are dense in $L^2(\mu)$ for any $\mu$ such that the moments $\int x^k d\mu$ do not grow too rapidly as $k \to \infty$. In this work, we…

The article develops techniques for solving equations G(x,y)=0, where G(x,y)=G(x_1,...,x_n,y) is a function in a given quasianalytic class (for example, a quasianalytic Denjoy-Carleman class, or the class of infinitely differentiable…

For functions belonging to the classes $C^{2}[0, 1]$ and $C^{3}[0, 1]$, we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness.…

We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of…

A result of Chernoff gives sufficient condition for an $L^2$-function on $\R^n$ to be quasi-analytic. This is a generalization of the classical Denjoy-Carleman theorem on $\R$ and of the subsequent work on $\R^n$ by Bochner and Taylor. In…

We provide a new characterization of quasi-analyticity of Denjoy-Carleman classes, related to \emph{Wetzel's Problem}. We also completely resolve which Denjoy-Carleman classes carry \emph{sparse systems}: if the Continuum Hypothesis (CH)…

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.

If F is an infinitely differentiable function whose composition with a blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N, where N_k =…

The paper is a continuation of our earlier article where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full…

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…

A space of analytic functions in the unit disc with uniformly continuous derivatives is said to be quasianalytic if the boundary value of a non-zero function from the class can not have a zero of infinite multiplicity. Such classes were…

Let $\mathcal C^M$ denote a Denjoy-Carleman class of $\mathcal C^\infty$ functions (for a given logarithmically-convex sequence $M = (M_n)$). We construct: (1) a function in $\mathcal C^M((-1,1))$ which is nowhere in any smaller class; (2)…

We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its…

Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show…

We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…