Ultradifferentiable extension theorems: A survey
نویسندگان
چکیده
We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney's classical theorem, with special emphasis on the existence continuous linear operators. The focus is Denjoy-Carleman classes for which we develop theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, a fair extent, elementary introduction Braun-Meise-Taylor based their representation intersections unions classes.
منابع مشابه
Hartogs Type Extension Theorems
Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...
متن کاملExtension Theorems without Dedekind Completeness
In the operator version of the Hahn-Banach-Kantorovich theorem, the range space Y is assumed to be Dedekind complete. Y. A. Abramovich and A. W. Wickstead improved this by assuming only the Cantor property on Y . Along the same line of reasoning, we obtained in this paper several new results of this type. We also see that assuming Cantor property on the domain spaces instead gives good results,...
متن کاملON NAKAYAMA'S EXTENSION OF THE x»<*> THEOREMS
where the a,are r fixed nonzero elements of Z, and 0<«i(a) <Ui(a) (i = 2, ■ ■ • , r), then A=Z. In [3, Theorem 11; 5; 2; l] specialized forms of (1) (e.g. cn(o) £Z, an(-a) —aEZ) are shown to imply commutativity at least for semi-simple rings. It is natural therefore to seek an extension of Nakayama's result to semi-simple rings. Since a semi-simple ring is a subdirect sum of primitive rings and...
متن کاملMeasure Extension Theorems for T0-spaces
The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent so...
متن کاملHahn-Banach extension theorems for multifunctions revisited
Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2022
ISSN: ['1878-0792', '0723-0869']
DOI: https://doi.org/10.1016/j.exmath.2021.12.001