Related papers: Th\'eor\`emes de Borel avec contraintes
This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
A Fej\'{e}r-type theorem is proved within the framework of $C^*$-algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a result on the structure of the relative commutant of a family…
A Liouville function is a complex analytic function H with a Taylor series \sum_{n=1}^{\infty} x^n/a_n such the a_n's form a ``very fast growing'' sequence of integers. In this paper we exhibit the complete first-order theory of the complex…
Extension to Walsh series of theorems of Helson and Katznelson on trigonometric series, saying that a trigonometric series whose partial sums are positive has its coefficients tend to zero but is not necessarily a Fourier-Lebesgue series
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
$\newcommand{\poly}{_{\operatorname{poly}}^{\bullet}}\newcommand{\td}{(\operatorname{td}_{L/A}^{\nabla})^{\frac{1}{2}}}\newcommand{\cx}[1]{\operatorname{tot}\big(\Gamma(\Lambda^\bullet…
In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…
The purpose of this expository note is to give a proof of a Schur-type theorem that characterizes the inner functions in terms of their Taylor coefficients. In view of Beurling's theorem, this provides a sequential characterization of the…
Let $X$ and $Y$ be the Hausdorff topological spaces and let $A$ be both an $\fs$- and $\gd$- subset of $X$. Let also $f\cn A\to Y$ be a function for which the inverse image of every open subset $U\subset Y$ is $\fs$ in $X$. We show that $f$…
For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the…
If the Continuum Hypothesis is false, it implies the existence of cardinalities between the integers and the real numbers. In studying these "cardinal characteristics of the continuum", it was discovered that many of the associated…
The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-Louveau show that with respect to Borel reducibility, any…
In this paper we study the development in Taylor series of the function $f(x)=x^x$. First section establishes a recursive relationship among successive derivatives of the function by using the coefficients defined therein. From recursion…
We show that if $\mathcal{F}$ is any "well-behaved" subset of the Borel functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $\pow(\mathbb{R})$ induced by $\mathcal{F}$ turns out to look like the Wadge hierarchy…
An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by…
A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…