Abstract
Abstract The previous three chapters were devoted to the general theory of strongly elliptic operators but this chapter is much more specific. Its aim is the analysis of second-order operators with real coefficients, and the main em phasis is on unimodular groups. The previous theory of course applied to second-order operators but they also have many characteristic features not shared by their higher-order counterparts. For example, Theorem 111.5.1 established that the semigroup kernel corresponding to a strongly elliptic operator is positive if, and only if, the operator is of second-order with real coefficients. This positivity is just one aspect of the special properties of the second-order operators. Dissipativity is another.
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