HIGHER-ORDER TRACE RELATIONS FOR SCHRODINGER-OPERATORS

We extend the trace formula recently proven for general one-dimensiona l Schrodinger operators which obtains the potential V(x) from a functi on xi(x, lambda) by deriving trace relations computing moments of xi(l ambda, x)d lambda in terms of polynomials in the derivatives of V at x . We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of xi associated with boundary conditions other than the Dirichlet boundary condition underlying xi.