This article is cited in 5 papers

On the Abel basis property of the system of root vector-functions of degenerate elliptic differential operators with singular matrix coefficients

K. Kh. Boimatov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan

Abstract: We establish completeness and summability in the Abel–Lidskii sense for the system of root vector-functions of nonselfadjoint elliptic matrix operators $A$ generated by noncoercive forms with the Dirichlet-type boundary conditions. An operator $A+\beta E$ is positive for a sufficiently large $\beta>0$ but not strongly positive in general. We obtain estimates for the eigenvalues and resolvent of $A$. Also, we study the resolvent of the extension$\mathscr{A}$ of $A$ to the corresponding negative space.

Keywords: Abel basis property, elliptic operator, root vector-function.

UDC: 517.918, 516.918

Received: 22.05.2002
Revised: 19.08.2004

 English version: Siberian Mathematical Journal, 2006, 47:1, 35–44

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