This article is cited in 5 papers

On basicity of eigenfunctions of second order discontinuous differential operator

B. T. Bilalov, T. B. Gasymov

Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ1141, Baku, Azerbaijan

Abstract: We consider a spectral problem for a second order discontinuous differential operator with spectral parameter in the boundary condition. We present a method for establishing the basicity of eigenfunctions for such problem. We also consider a direct expansion of a Banach space with respect to subspaces and we propose a method for constructing a basis for a space by the bases in subspaces. We also consider the cases when the bases for subspaces are isomorphic and the corresponding isomorphisms are not needed. The completeness, minimality and uniform minimality of the corresponding systems are studied. This approach has extensive applications in the spectral theory of discontinuous differential operators.

Keywords: eigenfunctions, basis, completeness, minimality, uniform minimality.

UDC: 517.984.2

Received: 13.02.2016

Language: English

 English version: Ufa Mathematical Journal, 2017, 9:1, 109–122

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