Spectral asymptotics for infinite order pseudo-differential operators

被引：3

作者：

Pilipovic, Stevan ^{[1
]}

Prangoski, Bojan ^{[2
]}

Vindas, Jasson ^{[3
]}

机构：

[1] Univ Novi Sad, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21000, Serbia

[2] Fac Mech Engn Skopje, Dept Math, Karposh 2 Bb, Skopje 1000, Macedonia

[3] Univ Ghent, Dept Math, Krijgslaan 281, B-9000 Ghent, Belgium

来源：

BULLETIN OF MATHEMATICAL SCIENCES | 2018年 / 8卷 / 01期

关键词：

Weyl asymptotic formula; Spectral asymptotics; Infinite order pseudo-differential operators; Hypoellipticity; Heat parametrix; Ultradistributions; TEMPERED ULTRADISTRIBUTIONS; SPACES;

D O I：

10.1007/s13373-017-0114-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral asymptotics are not of power-log-type but of log-type. The ultradistributional setting of such operators of infinite order makes the theory more complex so that the standard finite order global Weyl calculus cannot be used in this context.

引用

页码：81 / 120

页数：40

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