J Austral Math Soc Ser A 58 pp411--420, 1995.

Right Inverses of Vector Fields

George Virsik

Abstract

D. Przeworska-Rolewicz developed an algebra-based theory around linear, not necessarily continuous, operators D : X ® X which admit a right inverse, the elementary example being D = d/dt or, more generally, D = å^m_i=1 aⁱ¶/¶xⁱ where aⁱ are constants. We give conditions for the right invertability of D in the case where aⁱ are functions, or more generally, where D is the Lie or covariant derivative associated with a vector field on a (Banach) manifold M.

1991 AMS Subject Classification: 47D40, 58F99

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Authors

George Virsik

Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.