✦ LIBER ✦

An adiabatic theorem for section determinants of spectral projections

✍ Scribed by Peter Otte

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 202 KB
Volume: 278
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310254

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✦ Synopsis

Abstract

We derive an adiabatic‐type theorem that expresses the section determinants of spectral projections of a selfadjoint operator through the solution to an operator‐valued Wiener‐Hopf equation. The solution theory of this equation is developed and for a special case a concrete criterion that ensures uniqueness of the solution is presented. Furthermore, for a special class of operators a dichotomy criterion, which is used in the proof of the adiabatic theorem, is proved. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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