Abstract
In this chapter we introduce the notion of transmission property due to Boutet de Monvel which is a condition about symbols in the normal direction at the boundary. Elliptic boundary value problems cannot be treated directly by pseudo-differential operator methods. It was Boutet de Monvel who brought in the operator-algebraic aspect with his calculus in 1971. He constructed a relatively small “algebra”, called the Boutet de Monvel algebra, which contains the boundary value problems for elliptic differential operators as well as their parametrices.
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