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

Boundary triplets and the index of families of self-adjoint elliptic boundary problems