Third order operator with small periodic coefficients

2011/05/18 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:34A55 #msc:34B24 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1105.3545

10 pages

arxiv created 2011/05/18 · arxiv updated 2011/05/19

Abstract

We consider the third order operator with small 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers all real line. Under the minimal conditions on the coefficients we show that there are two possibilities: 1) The spectrum has multiplicity one except for a small spectral nonempty interval with multiplicity three. Moreover, the asymptotics of the small interval is determined. 2) All spectrum has multiplicity one only.

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