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Zbl 0716.35052
Shubin, M.A.
(Sjöstrand, J.)
Weak Bloch property and weight estimates for elliptic operators. Appendix: On the equality between weak and strong extensions (by M. A. Shubin and J. Sjöstrand). (English)
[J] Sémin. Équations Dériv. Partielles 1989-1990, No.5, 30 p. (1990).

The paper deals with the following problem. \par Let A denote a differential operator on a non-compact Riemannian manifold M, and assume that A defines an unbounded operator in the Hilbert space $L\sp 2(M)$. Assume that for some complex $\lambda$ we know a solution u of the equation $Au=\lambda u$, when can we conclude that $\lambda$ is in the spectrum $\sigma$ (A) of the operator A in $L\sp 2(M)?$ After an introduction with the main definitions and some preliminary lemmata, one considers weight estimates and decay of Green functions; then the third section deals with uniform properly supported pseudo-differential operators and structural inverse operators; and the last section contains some results related to the spectral properties of uniformly elliptic operators on manifolds of subexponential growth.
[G.Jumarie]

MSC 2000:: *35P05 General spectral theory of PDE
35J15 Second order elliptic equations, general
35S05 General theory of pseudodifferential operators

Keywords: Riemannian manifold; decay of Green functions; structural inverse operators; subexponential growth

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