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

Author:

Nikolai V. Ivanov

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Functional Analysis (math.FA)

journal:

date:

2023-06-26 16:00:00

Abstract

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.

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