Related papers: Ultradifferentiable extension theorems: a survey

We study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes can be viewed as weighted spaces of entire functions for…

We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows…

We study two classes of linear difference differential equations analogous to Euler-Cauchy ordinary differential equations, but in which multiple arguments are shifted forward or backward by fixed amounts. Special cases of these equations…

While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…

We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q-differential algebra. We study the first and higher order noncommutative differential calculus of…

We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…

Cartesian differential categories provide a categorical framework for multivariable differential calculus and also the categorical semantics of the differential $\lambda$-calculus. Taylor series expansion is an important concept for both…

Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…

The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized…

An analogue of Taylor's formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results…

In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial…

Universal theories are a broad class of well-motivated microscopic dynamics of the electroweak sector that go beyond the Standard Model description. The long distance physics is described by electroweak parameters which correspond to local…

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…

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…

This paper deals with extension of analytic covers. We prove topological extension theorems for analytic covers. The main result is an extension theorem which only uses the extension of the ramification divisor. We give also a Thullen-type…

We show a strong factorization theorem of Dixmier-Malliavin type for ultradifferentiable vectors associated with compact Lie group representations on sequentially complete locally convex Hausdorff spaces. In particular, this solves a…