On the Spectrum of Degenerate Operator Equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the Spectrum of Degenerate Operator Equations

Authors:	V. V. Kornienko

Affiliation:	(1) A. Navoi Samarkand State University, Uzbek SSR

Abstract:	We study the distribution in the complex plane of the spectrum of the operator , generated by the closure in $H = mathcal{L}_2 left( {0,b} right) otimes mathfrak{H}$ of the operation originally defined on smooth functions with values in a Hilbert space satisfying the Dirichlet conditions . Here $D_t equiv {d mathord{left/ {vphantom {d {dt}}} right. kern-nulldelimiterspace} {dt}}$ and A is a model operator acting in . Criterial conditions on the parameter for the eigenfunctions of the operator to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given.

Keywords:	degenerate partial differential equations boundary-value problem distribution of the spectrum generalized solution (in the sense of distributions) self-adjoint semibounded elliptic operator
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