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An adiabatic theorem for section determinants of spectral projections
Author(s) -
Otte Peter
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310254
Subject(s) - mathematics , adiabatic process , uniqueness , section (typography) , operator (biology) , spectral theorem , shift theorem , uniqueness theorem for poisson's equation , class (philosophy) , mathematical analysis , spectral theory of ordinary differential equations , picard–lindelöf theorem , pure mathematics , operator theory , danskin's theorem , fixed point theorem , quasinormal operator , finite rank operator , quantum mechanics , repressor , artificial intelligence , advertising , banach space , business , chemistry , computer science , biochemistry , transcription factor , physics , gene
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)