Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

被引：7

作者：

Boiti, Chiara ^{[1
]}

Jornet, David ^{[2
]}

Oliaro, Alessandro ^{[3
]}

Schindl, Gerhard ^{[4
]}

机构：

[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 30, I-44121 Ferrara, Italy

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, Camino Vera S-N, Valencia 46071, Spain

[3] Univ Torino, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin, Italy

[4] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2020年 / 15卷 / 01期

关键词：

Weight matrices; Ultradifferentiable functions; Sequence spaces; Nuclear spaces; PARTIAL-DIFFERENTIAL OPERATORS; PSEUDODIFFERENTIAL-OPERATORS;

D O I：

10.1007/s43037-020-00090-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.

引用

页数：39

共 41 条

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[Anonymous], 1964, APPL HARMONIC ANAL

[2]

[Anonymous], 1972, NUCL LOCALLY CONVEX

[3] Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions [J].