A shortwave source near a smooth, convex hypersurface and the spectral function of the Laplace operator on a Riemannian manifold

Abstract

Remark 3. The present scheme of defining "boundary" conditions on submanifolds of large codimension, based on the study of traces (in the sense of generalized functions of the appropriate class) of functions in the domain of the adjoint operator on parallel and nearby submanifolds, is apparently applicable to a broader class of elliptic differential (and pseudodif ferential) operators.7he author wishes to thank A. S. Blagoveshchenskii for his constant attention to the work and for useful suggestions.