General spectral flow formula for fixed maximal domain

• Autorzy: Bernhelm Booss-Bavnbek , Chaofeng Zhu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Spectral flow; Maslow index; elliptic boundary value problems; 58J30; 53D12

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 3
• Strony: 558-577

Daty

wydano

2005-09-01

online

2005-09-01

Twórcy

autor

Bernhelm Booss-Bavnbek

• Roskilde University

autor

Chaofeng Zhu

• Nankai University

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475923