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On the Riesz Inequality and the Basis Property of Systems of Root Vector Functions of a Discontinuous Dirac Operator

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Abstract

We consider a discontinuous Dirac operator on the interval (0, 2π). It is assumed that its coefficient (potential) is a complex-valued matrix function integrable on (0, 2π). Criteria are established for the Riesz and unconditional basis properties of the system of root vector functions in L 22 (0, 2π). A theorem about the equivalent basis property in L 2 p (0, 2π), 1 < p > ∞, is proved.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AZ, 1141, Azerbaijan

    V. M. Kurbanov

  2. Azerbaijan State Pedagogical University, Baku, AZ, 1000, Azerbaijan

    V. M. Kurbanov & L. Z. Buksaeva

Authors
  1. V. M. Kurbanov
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  2. L. Z. Buksaeva
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Correspondence to V. M. Kurbanov or L. Z. Buksaeva.

Additional information

Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 8, pp. 1079–1089.

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Kurbanov, V.M., Buksaeva, L.Z. On the Riesz Inequality and the Basis Property of Systems of Root Vector Functions of a Discontinuous Dirac Operator. Diff Equat 55, 1045–1055 (2019). https://doi.org/10.1134/S0012266119080056

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  • DOI: https://doi.org/10.1134/S0012266119080056

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