Geodesic
On the spectra of first order irregular operator equations
Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1213-1234 Cet article a éte moissonné depuis la source Math-Net.Ru

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The distribution of the spectrum $\sigma L=P\sigma L\cup C\sigma L\cup R\sigma L$ of the operator $L=L(\mu ,\alpha ,a,A)$ in the complex plane $\mathbb C$ is studied. The operator $L$ is the closure in $H=\mathscr L_2(0,b)\otimes \mathfrak H$ of the operator $t^\alpha aD_t+A$ originally defined on smooth functions $u(t)\colon [0,b]\to \mathfrak H$ satisfying the condition $\mu u(0)-u(b)=0$, where $\alpha \in \mathbb R$, $a\in \mathbb C$, $D_t\equiv d/dt$, $A$ is a model operator in a Hilbert space $\mathfrak H$ and $\mu \in \overline {\mathbb C}$. Conditions (criteria) in terms of the parameter $\alpha$ ensuring that the eigenfunctions of the operator $L\colon H\to H$ make up a complete system, a minimal system, or a (Riesz) basis in the Hilbert space $H$ are obtained. 
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     author = {V. V. Kornienko},
     title = {On the spectra of first order irregular operator equations},
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     volume = {188},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_8_a7/}
}
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V. V. Kornienko. On the spectra of first order irregular operator equations. Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1213-1234. http://geodesic.mathdoc.fr/item/SM_1997_188_8_a7/

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