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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1111–1131 | Cite as

Eigenfunctions of Periodic Differential Operators Analytic in a Strip

  • Robert CarlsonEmail author
Article
  • 28 Downloads

Abstract

Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy–Hilbert space of analytic functions with inner product defined by integration over a period on the boundary of the strip. Simple examples show that eigenfunctions may form a complete set for a narrow strip, but completeness may be lost for a wide strip. Completeness of the eigenfunctions in the Hardy–Hilbert space is established for regular second order operators with matrix-valued coefficients when the leading coefficient satisfies a positive real part condition throughout the strip.

Keywords

Eigenfunction expansion Periodic differential operator Hardy space Semigroup generators 

Mathematics Subject Classification

34L10 34M03 47D06 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Colorado at Colorado SpringsColorado SpringsUSA

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