Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Furdos, Stefan¹  Nenning, David Nicolas²  Rainer, Armin^2,3  Schindl, Gerhard² 

[1] Masaryk Univ, Dept Math & Stat, Kotlarska 2, CS-61137 Brno, Czech Republic

[2] Universitat Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] Univ Educ Lower Austria, Campus Baden Muhlgasse 67, A-2500 Baden, Austria

关键词: Almost analytic extensions;    Ultradifferentiable classes;    Ultradifferentiable wave front set;    Boundary values;    Elliptic regularity;    Uniqueness of distributions;   

DOI  :  10.1016/j.jmaa.2019.123451

来源: Elsevier

【 摘 要 】

We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the (partial derivative) over bar -derivative near the real domain. We work in a general uniform framework which comprises the main classical ultradifferentiable classes but also allows to treat unions and intersections of such. The second part of the paper is devoted to applications in microlocal analysis. The ultradifferentiable wave front set is defined in this general setting and characterized in terms of almost analytic extensions and of the FBI transform. This allows to extend its definition to ultradifferentiable manifolds. We also discuss ultradifferentiable versions of the elliptic regularity theorem and obtain a general quasianalytic Holmgren uniqueness theorem. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free