  The paper is devoted to an abstract axiomatic version of a construction of
boundary triplets implicit in the works of M.I. Vishik and G. Grubb and its
applications to the index of families of self-adjoint elliptic differential
boundary problems of order one. This leads to an analytic proof of the index
theorem for Dirac-like self-adjoint boundary problems from arXiv:2207.09574,
and to an Agranovich-Dynin type theorem computing the difference of indices of
families of self-adjoint boundary problems differing only by the boundary
conditions.
