Construction of KdV Flow I. τ-Function via Weyl Function

摘要

Sato introduced the -function to describe solutions to a wide class ofcompletely integrable differential equations. Later Segal–Wilson representedit in terms of the relevant integral operators on Hardy space of the unitdisc. This paper gives another representation of the -functions by the Weylfunctions for 1d Schr¨odinger operators with real valued potentials, whichwill make it possible to extend the class of initial data for the KdV equationto more general one.