94-77 Gesztesy F., Holden H., Simon B., Zhao Z.

Higher Order Trace Relations for Schrodinger Operators (66K, AMSTeX) Mar 30, 94

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Abstract. We extend the trace formula recently proven for general one-dimensional Schr\"odinger operators which obtains the potential $V(x)$ from a function $\xi(x, \lambda)$ by deriving trace relations computing moments of $\xi(x, \lambda)\,d\lambda$ 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 $\xi$.

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