Global functional calculus for operators on compact Lie groups

被引：24

作者：

Ruzhansky, Michael ^{[1
]}

Wirth, Jens ^{[2
,3
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Munich, Math Inst, D-80333 Munich, Germany

[3] Univ Stuttgart, Inst Anal Dynam & Modellierung, D-70569 Stuttgart, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Functional calculus; Pseudo-differential operators; Compact Lie groups; Garding inequality; COMPLEX POWERS; DIFFERENTIAL-OPERATORS; MANIFOLDS;

D O I：

10.1016/j.jfa.2014.04.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex powers of such operators. As an application, we give a constructive symbolic proof of the Carding inequality for operators in (rho, delta)-classes in the setting of compact Lie groups. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：144 / 172

页数：29

共 25 条

[1]

[Anonymous], 1984, ASTERISQUE

[2]

[Anonymous], 2010, BACKGROUND ANAL ADV

[3] CHARACTERIZATION OF PSEUDODIFFERENTIAL OPERATORS AND APPLICATIONS [J].

BEALS, R .

DUKE MATHEMATICAL JOURNAL, 1977, 44 (01) :45-57

[4] UNITARY REPRESENTATIONS OF LIE-GROUPS AND GARDINGS INEQUALITY [J].

BRATTELI, O ;

GOODMAN, FM ;

JORGENSEN, PET ;

ROBINSON, DW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 107 (03) :627-632

[5] Complex powers of hypoelliptic pseudodifferential operators [J].

Buzano, Ernesto ;

Nicola, Fabio .

JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 245 (02) :353-378

[6] Bounded imaginary powers of differential operators on manifolds with conical singularities [J].

Coriasco, S ;

Schrohe, E ;

Seiler, J .

MATHEMATISCHE ZEITSCHRIFT, 2003, 244 (02) :235-269

[7]

Dasgupta A., 2014, B SCI MATH

[8]

Dasgupta A., 2014, J ANAL MATH IN PRESS

[9]

Delgado J., 2013, J MATH PURES APPL

[10]

Kumano-go H., 1973, OSAKA J MATH, V10, P147

← 1 2 3 →