caa a22 4500 475740696 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026615423129 doi (NATIONALLICENCE)springer-10.1023/A:1026615423129 Kornienko V. A. Navoi Samarkand State University, Uzbek SSR aut On the Spectrum of Degenerate Operator Equations [Elektronische Daten] [V. Kornienko] We study the distribution in the complex plane $$\mathbb{C}$$ of the spectrum of the operator $$L = L\left( {\alpha ,a,A} \right),{\text{ }}\alpha \in \mathbb{R},{\text{ }}\alpha \in \mathbb{C}$$ , generated by the closure in $$H = \mathcal{L}_2 \left( {0,b} \right) \otimes \mathfrak{H}$$ of the operation $$t^\alpha aD_t^2 + A$$ originally defined on smooth functions $$u\left( t \right):\left[ {0,b} \right] \to \mathfrak{H}$$ with values in a Hilbert space $$\mathfrak{H}$$ satisfying the Dirichlet conditions $$u\left( 0 \right) = u\left( b \right) = 0$$ . Here $$D_t \equiv {d \mathord{\left/ {\vphantom {d {dt}}} \right. \kern-\nulldelimiterspace} {dt}}$$ and A is a model operator acting in $$\mathfrak{H}$$ . Criterial conditions on the parameter $$\alpha$$ for the eigenfunctions of the operator $$L:H \to H$$ to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. Plenum Publishing Corporation, 2000 degenerate partial differential equations nationallicence boundary-value problem nationallicence distribution of the spectrum nationallicence generalized solution (in the sense of distributions) nationallicence self-adjoint semibounded elliptic operator nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 576-587 0001-4346 68:5-6<576 2000 68 11006 https://doi.org/10.1023/A:1026615423129 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026615423129 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kornienko V. A. Navoi Samarkand State University, Uzbek SSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 576-587 0001-4346 68:5-6<576 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer