Hilbert-Schmidt and trace class pseudo-differential operators on the Heisenberg group

被引：11

作者：

Dasgupta, Aparajita ^{[1
]}

Wong, M. W. ^{[2
]}

机构：

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

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2013年 / 4卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Heisenberg group; Stone-von Neumann theorem; Fourier transform; Fourier inversion formula; lambda-Weyl transforms; Pseudo-differential operators; Operator-valued symbols; L-2-boundedness; Hilbert-Schmidt operators; Trace class operators; Traces;

D O I：

10.1007/s11868-013-0079-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Pseudo-differential operators with operator-valued symbols on the Heisenberg group H-n are introduced. We give necessary and sufficient conditions on the symbols for which these operators are in the Hilbert-Schmidt class. These Hilbert-Schmidt operators are then identified with Weyl transforms with symbols in L-2(R2n+1 x R2n+1). We also give a characterization of trace class pseudo-differential operators on the Heisenberg group H-n. A trace formula for these trace class operators is presented.

引用

页码：345 / 359

页数：15

共 12 条

[1]

[Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals

[2]

[Anonymous], 1980, FUNCTIONAL ANAL

[3]

Andres RTC, 2011, J PSEUDO-DIFFER OPER, V2, P367, DOI 10.1007/s11868-011-0035-4

[4]

Chen Z, 2013, J PSEUDO-DIFFER OPER, V4, P13, DOI 10.1007/s11868-013-0061-5

[5]

Du J., 2000, APPROX THEORY APPL N, V16, P41

[6]

Fischer V., ARXIV12092621

[7] Lower bounds for operators on graded Lie groups [J].

Fischer, Veronique ;

Ruzhansky, Michael .

COMPTES RENDUS MATHEMATIQUE, 2013, 351 (1-2) :13-18

[8]

Molahajloo S, 2010, J PSEUDO-DIFFER OPER, V1, P183, DOI 10.1007/s11868-010-0010-5

[9]

Thangavelu S, 1998, HARMONIC ANAL HEISEN

[10]

Wong M.W., 1998, Weyl Transforms

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