### Resumé

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

*Central European Journal of Mathematics*,

*3*(3), 558-577.

}

*Central European Journal of Mathematics*, bind 3, nr. 3, s. 558-577.

**General spectral flow formula for fixed maximal domain.** / Booss-Bavnbek, Bernhelm; Zhu, Chaofeng.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - General spectral flow formula for fixed maximal domain

AU - Booss-Bavnbek, Bernhelm

AU - Zhu, Chaofeng

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Spectral flow, Maslov index, elliptic boundary value problems

M3 - Journal article

VL - 3

SP - 558

EP - 577

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

SN - 1895-1074

IS - 3

ER -