Related papers: The Kohn Algorithm on Denjoy-Carleman Classes

Let F be a class of functions with the uniqueness property: if a function f in F vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a quantitative version of this property, e.g. a…

We introduce a new class of commutative {non-noetherian} rings, called $n$-subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. For an integer $n \ge 0$, the ring $R$ is $n$-subperfect if…

We prove here the Wolff-Denjoy-type theorem for a very large class of pseudoconvex domains in $\mathbb C^n$ that may contain many classes of pseudoconvex domains of finite type and infinite type.

Inspired by the construction of the Cuntz semigroup for a C*-algebra, we introduce the matrix Malcolmson semigroup and the finitely presented module Malcolmson semigroup for a unital ring. These two semigroups are shown to have isomorphic…

This article chronicles a development that started around 1990 with \cite{BoasStraube91}, where the authors showed that if a smooth bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ admits a defining function that is plurisubharmonic…

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…

Let $N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular $\omega$-curve $\mathbb{R}^n \to N$ with infinite energy. We prove that, if the de Rham class of $\omega$ is non-zero and belongs to a so-called…

Semi-free ideal rings, or semifirs, were introduced by Paul M. Cohn to study universal localizations in the non-commutative setting. We provide new examples of semifirs consisting of analytic functions in several non-commuting variables.…

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 give a generalization of the classical Bombieri--Schneider--Lang criterion in transcendence theory. We give a local notion of $LG$--germ, which is similar to the notion of $E$-- function and Gevrey condition, and which generalize (and…

We prove the existence of approximate solutions in the (regular) Denjoy-Carleman sense for some systems of smooth complex vector fields. Such approximate solutions provide a well defined notion of Denjoy-Carleman wave front set of…

We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert-Schmidt bounded type, are locally $m$-convex Fr\'echet algebras. We prove that the spectrum of these algebras…

We prove a version of Axler-Zheng's Theorem on smooth bounded pseudoconvex domains in C^n on which the dbar-Neumann operator is compact.

We introduce the Colombeau Quaternio Algebra and study its algebraic structure. We also study the dense ideal, dense in the algebraic sense, of the algebra of Colombeau generalized numbers and use this show the existence of a maximal ting…

In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in \'etale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of…

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…

The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We show arithmetic…

Multivariate versions of the Kronecker theorem in the continuous multivariate setting has recently been published. These theorems characterize the symbols that give rise to finite rank multidimensional Hankel and Toeplitz type operators…

We expand the notion of core to $cl$-core for Nakayama closures $cl$. In the characteristic $p>0$ setting, when $cl$ is the tight closure, denoted by *, we give some examples of ideals when the core and the *-core differ. We note that…

An $L^2$ version of the classical Denjoy-Carleman theorem regarding quasi-analytic functions was proved by P. Chernoff on $\mathbb R^n$ using iterates of the Laplacian. We give a simple proof of this theorem which generalizes the result on…