On the Relationship of Some Results of Gelfand-Dikii and P. Moerbeke, and a Natural Trace Functional for Formal Asymptotic Pseudo-Differential Operators.

摘要

This paper developed out of an attempt to understand results of Gelfand-Dikii and P. Moerbeke in a unified way. A natural abstract setting is provided for understanding the symplectic structure involved in both results. The setting is an orbit in the dual algebra of a group. A natural trace functional for formal asymptotic pseudo-differential operators are discussed, as well as so-called Lenard recursion relations inherent in these structures.