On Bessel property and unconditional basicity of the systems of root vector-functions of a Dirac type operator

Vali M. Kurbanov, Elchin J. Ibadov, Gunel R. Hajiyeva

Abstract


In the paper we consider Dirac type one-dimensional operator Dy=B(dy)/(dx) +P(x y, y x)=(y1(x),y2 (x))T, where B=(0      b1b2     0

;    b1 >0,    b2 <0, P(x)=

(

      p1 \(x)          0            0            p2 (x)

)

, moreover p1 \(x) and p2 (x) are complex-valued functions determined on arbitrary finite interval G(a,b) by a real straightline, and establish the criterion of Bessel property and unconditional basicity of the system of root vector-functions of this operator.


Keywords


Bessel inequality, unconditional basicity, root vector-functions

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