RELLICH TYPE DECAY THEOREM FOR EQUATION P(D)U=F WITH F SUPPORTED IN INFINITE CYLINDERS

In this paper we prove that for a certain class of linear differential operators P(partial derivative/i partial derivative x) if P(partial d erivative/i partial derivative x) u(x) has support inside a convex inf inite cylinder and decays exponentially to zero in one direction of th e cylinder, then u(x) must have support inside the same cylinder provi ded that u(x) satisfies a certain Rellich type decay condition at infi nity. Some examples are given, including the reduced wave equation and the reduced system of crystal optics.