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 this paper, we consider Dirac type one-dimensional operator $Dy=B\frac{dy}{dx} +P\left(x\right)y$, $y\left(x\right)=\left(y_{1} \left(x\right),y_{2} \left(x\right)\right)^{T} $, where $B=\left(\begin{array}{l} {0\, \, \, b_{1} } \\ {b_{2} \, \, 0} \end{array}\right)\, ;\, \, b_{1} >0,\, \, b_{2} <0$, $P\left(x\right)=\left(\begin{array}{l} {\, \, \, p_{1} \left(x\right)\, \, \, \, \, 0} \\ {\, \, \, \, \, \, 0\, \, \, \, \, \, p_{2} \left(x\right)} \end{array}\right),$ $p_{1} \left(x\right)$ and $p_{2} \left(x\right)$ are complex-valued functions defined on arbitrary finite interval $G\left(a,b\right)$ of 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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References


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