Some Results on Ordinary Differential Operators with Periodic\n Coefficients

2014/12/14 by Vassilis G. Papanicolaou, Papanicolaou, Vassilis G.
Computer Science · Mathematics · #34B10 #47A75 #47E05 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1412.5423

openalex publication_date 2014/12/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

For a general ordinary differential operator \L with periodic\ncoefficients we prove that the characteristic polynomial of the Floquet matrix\nis irreducible over the field of meromorphic functions. We also consider a\nmultipoint eigenvalue problem and show that its eigenspaces are spanned by pure\nor generalized Floquet solutions. Finally, at the end of the paper we mention\nsome relevant conjectures and open questions.\n

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