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 L22(0, 2π). A theorem about the equivalent basis property in Lp2(0, 2π), 1 < p > ∞, is proved.

About the authors

V. M. Kurbanov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences; Azerbaijan State Pedagogical University

Author for correspondence.
Email: q.vali@yahoo.com
Azerbaijan, Baku, AZ, 1141; Baku, AZ, 1000

L. Z. Buksaeva

Azerbaijan State Pedagogical University

Author for correspondence.
Email: leylabuksayeva.80@yahoo.com
Azerbaijan, Baku, AZ, 1000

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