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

2023/06/27 by Nikolai V. Ivanov, Ivanov, Nikolai V. · 1 citation
Computer Science · Mathematics · #19K56 (Primary) #47A53 #47F10 (Secondary) #58J20 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2306.15132

openalex publication_date 2023/06/27 · openalex created_date 2023/06/30 · openalex updated_date 2026/07/28

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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