Abstract
We describe a method for obtaining estimates at infinity for eigenfunctions of integral operators of certain classes in unbounded domains of . We consider integral operators whose kernels can be written in the form , , where for some functions and satisfying certain natural additional conditions. We show that if the operator with the corresponding kernel is Noetherian in and the coefficients , satisfy certain conditions, then the solutions of belong to the weighted space . The method is applied to obtain exponential estimates for eigenfunctions of -particle Schrödinger operators and estimates of decay at infinity for the solutions of convolution-type equations with variable coefficients.
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