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On the Abel Basis Property of the System of Root Vector-Functions of Degenerate Elliptic Differential Operators with Singular Matrix Coefficients

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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 + βE is positive for a sufficiently large β > 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 \(A\) of A to the corresponding negative space.

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  1. Institute of Mathematics, Dushanbe, Tajikistan

    K. Kh. Boimatov

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  1. K. Kh. Boimatov
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__________

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 46–57, January–February, 2006.

Original Russian Text Copyright © 2006 Boimatov K. Kh.

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Boimatov, K.K. On the Abel Basis Property of the System of Root Vector-Functions of Degenerate Elliptic Differential Operators with Singular Matrix Coefficients. Sib Math J 47, 35–44 (2006). https://doi.org/10.1007/s11202-006-0004-y

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  • DOI: https://doi.org/10.1007/s11202-006-0004-y

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