Spectral Properties of Some Linear Matrix Differential Operators in Lp-spaces on $${\mathbb{R}}$$ |
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Authors: | E Albrecht W J Ricker |
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Institution: | 1.Fachrichtung 6.1 – Mathematik,Universit?t des Saarlandes,Saarbrücken,Germany;2.Mathematisch-Geographische Fakult?t,Katholische Universit?t Eichst?tt–Ingolstadt,Eichst?tt,Germany |
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Abstract: | A detailed study is made of matrix-valued, ordinary linear differential operators T in for 1 < p < ∞, which arise as the perturbation of a constant coefficient differential operator of order n ≥ 1 by a lower order differential operator which has a factorisation S = AB for suitable operators A and B. Via techniques from L
p
-harmonic analysis, perturbation theory and local spectral theory, it is shown that T satisfies certain local resolvent estimates, which imply the existence of local functional calculi and decomposability properties
of T.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47A60 47B40 Secondary 47F05 |
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