On Whitney’s extension theorem for ultradifferentiable functions

被引:0
作者
Manuel Valdivia
机构
[1] Universidad de Valencia,Departamento de Análisis Matemático
来源
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas | 2011年 / 105卷
关键词
Whitney jet; Ultradistributions; 46F05; 46F20;
D O I
暂无
中图分类号
学科分类号
摘要
Let M be a Whitney-regular bounded subset in the k-dimensional Euclidean space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^k}$$\end{document} . We show in this article that certain jets of functions defined in the closure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{M}}$$\end{document} of M are Whitney jets, either of Beurling type, or of Roumieu type, and as a consequence we give some results related with Whitney’s extension theorem. We also obtain some structure theorems for ultradistributions T with support contained in a compact K, in terms of Borel measures concentrated at K.
引用
收藏
页码:339 / 357
页数:18
相关论文
共 20 条
[1]  
Bonet J.(1991)Whitney’s extension theorem for non quasianalytic functions Studia Math. 99 156-184
[2]  
Braun R.W.(1989)Whitney’s extension theorem for ultradifferentiable functions of Roumieu type Proc. R. Ir. Acad. 89 53-66
[3]  
Meise R.(1990)Ultradifferentiable functions and Fourier analysis Results Math. 17 206-237
[4]  
Taylor B.A.(1980)An extension theorem of Whitney type for non-quasianalytic classes of functions J. Lond. Math. Soc. 22 495-505
[5]  
Bonet J.(1994)Surjectivité de l’application restriction à un compact dans les classes de fonctions ultradifferéntiables Math. Ann. 298 7-40
[6]  
Meise R.(1973)Ultradistributions I, structure theorems and a characterization J. Fac. Sci. Univ. Tokyo, Sec. I A Math. 20 25-105
[7]  
Taylor B.A.(1988)Whitney’s extension theorem for ultradifferentiable functions of Beurling type Ark Mat. 26 265-287
[8]  
Braun R.W.(2008)On the structure of the ultradistributions of Beurling type RACSAM, Rev. R. Acad. Cien. Serie A. Mat. 102 221-235
[9]  
Meise R.(2009)On the structure of certain ultradistributions RACSAM, Rev. R. Acad. Cien. Serie A. Mat. 103 17-48
[10]  
Taylor B.A.(1934)Functions differentiable on the boundaries of regions Ann. Math. 35 482-485