Differential Operator Matrices of Mixed Order with Periodic Coefficients

  • R. Hryniv
  • A. Shkalikov
  • A. Vladimirov
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)


We study spectral properties of 2 x 2 operator matrices H defined in the Hilbert space ℍ = L 2(R) x L 2(R)by linear differential systems of mixed order with periodic coefficients. We prove that the spectrum σ (H) of H has a band and gap structure and consists of two band sequences one of which, when infinite, has a finite accumulation point, and give sufficient conditions for this accumulation to take place.

AMS Subject Classification

47A10 47E05 34B05 34L05 


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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • R. Hryniv
    • 1
  • A. Shkalikov
    • 2
  • A. Vladimirov
  1. 1.Institute for Applied Problems of Mechanics and MathematicsLvivUkraine
  2. 2.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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