Some Sharp L2 Inequalities for Dirac Type Operators

被引：3

作者：

Balinsky, Alexander ^{[1
]}

Ryan, John ^{[2
]}

机构：

[1] Cardiff Univ, Cardiff Sch Math, Cardiff 24 4AG, S Glam, Wales

[2] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷

关键词：

Dirac operator; Clifford algebra; conformal Laplacian; Paenitz operator;

D O I：

10.3842/SIGMA.2007.114

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the spectra of Dirac type operators on the sphere S-n to produce sharp L-2 inequalities on the sphere. These operators include the Dirac operator on Sn, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in R-n.

引用

页数：10

共 16 条

[1]

AHLFORS LV, 1984, ANN ACAD SCI FENN-M, V9, P93

[2]

[Anonymous], 1982, RES NOTES MATH

[3] SHARP SOBOLEV INEQUALITIES ON THE SPHERE AND THE MOSER-TRUDINGER INEQUALITY [J].

BECKNER, W .

ANNALS OF MATHEMATICS, 1993, 138 (01) :213-242

[4]

BOJARSKI B, 1989, P 20 IR MATH C TEHR

[5] Spontaneous generation of eigenvalues [J].

Branson, Thomas ;

Orsted, Bent .

JOURNAL OF GEOMETRY AND PHYSICS, 2006, 56 (11) :2261-2278

[6]

CALDERBANK DMJ, 1997, DIRAC OPERATORS CLIF

[7]

CNOPS J, 1995, TEXTOS MATEMATICA B

[8]

Davies EB, 1998, MATH Z, V227, P511, DOI 10.1007/PL00004389

[9] The kernel of dirac operators on S3 and R3 [J].

Erdós, L ;

Solovej, JP .

REVIEWS IN MATHEMATICAL PHYSICS, 2001, 13 (10) :1247-1280

[10]

LIEB E, 2001, GRADUATE TEXTS MATH, V14

← 1 2 →