On linear, additive, and homogeneous operators in idempotent analysis

1992 ◽  
pp. 87-102 ◽  
Author(s):  
V. Kolokoltsov
Keyword(s):  
Idempotent Analysis ◽  
Homogeneous Operators

First Order Operators on Manifolds With a Group Action

1996 ◽  
Vol 48 (4) ◽  
pp. 758-776 ◽  
Author(s):  
H. D. Fegan ◽  
B. Steer
Keyword(s):  
Differential Operator ◽  
Group Action ◽  
Lie Group ◽  
Differential Operators ◽  
Order Differential Operator ◽  
Compact Lie Group ◽  
First Order ◽  
Rank 2 ◽  
Homogeneous Operators

AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.

Idempotent Analysis and Its Applications

1997 ◽  
Author(s):  
Vassili N. Kolokoltsov ◽  
Victor P. Maslov
Keyword(s):  
Idempotent Analysis
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