Abstract
An operator norm estimate of the Green operator for the Laplace equation on an open set in the Euclidean space is given in terms of capacity. This applies to the perturbation of the Green function for the Schrodinger equation. A sufficient condition for the Green function for the Schrodinger equation to have decay near the boundary comparable to that for the Laplace equation is given in terms of an integrable condition for the potential of the Schrodinger equation. This has an application to the Martin boundary of a smooth domain with respect to the Schrodinger equation. Also, it is related to the Cranston-McConnell inequality about the life time estimate and the integrability of nonnegative superharmonic functions. 1991 Mathematics Subject Classification. 31A35, 31B35, 31C35.
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