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Sato introduced the tau-function to describe solutions to a wide class ofcompletely integrable differential equations. Later Segal-Wilson represented itin terms of the relevant integral operators on Hardy space of the unit disc.This paper gives another representation of the tau-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.

Construction of KdV flow I. Tau function via Weyl function