Bojarski’s Theorem. General Linear Conjugation Problems

Abstract

We recover the index of a Dirac operator A over a closed partitioned manifold M =X ₊ ∪ X ₋ with ∂X ₊ = ∂X ₋ = X ₊ ∩ X ₋ = Y from the Fredholm pair of Cauchy data spaces along Y. Similarly, the index of the linear conjugation (or transmission) problem As _± = 0 in X±\Y and s ₋|y = Φ (s ₊ |y) is given by twisting the Cauchy data spaces with Φ. Related local elliptic boundary conditions for systems of Dirac operators are considered