On the spectral theory of second-order elliptic differential operators

$(L^p,\,L^q)$-estimates and $\mathfrak S_p$-properties of powers of the resolvent in weighted $L^p$-spaces are studied for a certain selfadjoint realization of the formal differential expression $-\sum_{k,j}\partial_k a_{kj}\partial_j+V$. A theory of generalized eigenfunction expansions is developed, and the continuous spectrum is investigated.
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