Malgrange division by quasianalytic functions
| Autor: | Pierre D. Milman, Edward Bierstone |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Model theory
Class (set theory) Pure mathematics Mathematics::Complex Variables Generalization General Mathematics Analytic continuation 010102 general mathematics Mathematics::Classical Analysis and ODEs Structure (category theory) Division (mathematics) 16. Peace & justice 01 natural sciences Bounded function 0103 physical sciences 010307 mathematical physics 0101 mathematics Analytic function Mathematics |
| Zdroj: | Journal of the London Mathematical Society. 95:725-741 |
| ISSN: | 0024-6107 |
| DOI: | 10.1112/jlms.12032 |
| Popis: | 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 analysis of linear partial differential equations) and the class of infinitely differentiable functions that are definable in a polynomially bounded o-minimal structure (of origin in model theory). We prove a generalization to quasianalytic functions of Malgrange's celebrated theorem on the division of infinitely differentiable by real-analytic functions. |
| Databáze: | OpenAIRE |
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