An analytic formula for the index of an elliptic boundary-value problem

An expression is obtained for an elliptic boundary-value problem $(A,B)$ in the form of a sum of two terms, one of which depends only on the properties of the operator $A$ at interior points of the domain, while the second depends on properties of $A$ and $B$ on the boundary. Each term is the difference of the traces of operators effectively constructed from $A$ and $B$.
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