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On the Ries inequality and the basicity of systems of root vector functions of $2m$th order Dirac-type operator with summable coefficient

E. J. Ibadov

Azerbaijan State Pedagogical University Baku, 68 Uzeyir Hajibeyov str., Baku, AZ1000 Republic of Azerbaijan

Abstract: We consider a Dirac-type operator of $2m$th order on a finite interval $G=(a,b).$ It is assumed that its coefficient is a complex-valued matrix function summable on $G=(a,b)$. A Riesz property criterion is established for a system of root vector functions, and a theorem on the equivalent basis property in $L_{p}^{2m} (G), \ 1<p<\infty $ is proved.

Keywords: operator of Dirac-type, root vector function, Riesz inequality, equivalent basis property.

UDC: 517

Received: 30.12.2023
Revised: 05.05.2024
Accepted: 26.06.2024

DOI: 10.26907/0021-3446-2024-11-23-34

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:11, 18–28