### Abstract

We consider a continuous curve of linear elliptic formally
self-adjoint differential operators of first order with smooth
coefficients over a compact Riemannian manifold with boundary
together with a continuous curve of global elliptic boundary value
problems. We express the spectral flow of the resulting continuous
family of (unbounded) self-adjoint Fredholm operators in terms of
the Maslov index of two related curves of Lagrangian spaces. One
curve is given by the varying domains, the other by the Cauchy
data spaces. We provide rigorous definitions of the underlying
concepts of spectral theory and symplectic analysis and give a
full (and surprisingly short) proof of our General Spectral Flow
Formula for the case of fixed maximal domain. As a side result, we
establish local stability of weak inner unique continuation
property (UCP) and explain its role for parameter dependent
spectral theory.

Originalsprog | Engelsk |
---|---|

Tidsskrift | Central European Journal of Mathematics |

Vol/bind | 3 |

Udgave nummer | 3 |

Sider (fra-til) | 558-577 |

Antal sider | 20 |

ISSN | 1895-1074 |

Status | Udgivet - 2005 |

## Citer dette

Booss-Bavnbek, B., & Zhu, C. (2005). General spectral flow formula for fixed maximal domain.

*Central European Journal of Mathematics*,*3*(3), 558-577.