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Mat. Zametki, 2000, Volume 68, Issue 5, Pages 677–691 (Mi mz989)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Spectrum of Degenerate Operator Equations

V. V. Kornienko

A. Navoi Samarkand State University

Abstract: We study the distribution in the complex plane $\mathbb C$ of the spectrum of the operator $L=L(\alpha,a,A)$, $\alpha\in\mathbb R$, $a\in\mathbb C$, generated by the closure in $H=\mathscr L_2(0,b)\otimes\mathfrak H$ of the operation $t^\alpha aD_t^2+A$ originally defined on smooth functions $u(t)\colon[0,b]\to\mathfrak H$ with values in a Hilbert space $\mathfrak H$ satisfying the Dirichlet conditions $u(0)=u(b)=0$. Here $D_t\equiv d/dt$ and $A$ is a model operator acting in $\mathfrak H$. Criterial conditions on the parameter $\alpha$ for the eigenfunctions of the operator $L\colon H\to H$ to form a complete and minimal system as well as a Riesz basis in the Hilbert space $H$ are given.

DOI: https://doi.org/10.4213/mzm989

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English version:
Mathematical Notes, 2000, 68:5, 576–587

Bibliographic databases:

UDC: 517.95
Received: 06.03.1997
Revised: 30.11.1999

Citation: V. V. Kornienko, “On the Spectrum of Degenerate Operator Equations”, Mat. Zametki, 68:5 (2000), 677–691; Math. Notes, 68:5 (2000), 576–587

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. P. Tepoyan, H. S. Grigoryan, “On degenerate nonself-adjoint differential equations of fourth order”, Uch. zapiski EGU, ser. Fizika i Matematika, 2012, no. 3, 29–33  mathnet
    2. L. Tepoyan, “Nonselfadjoint degenerate differential equations of higher order”, Uch. zapiski EGU, ser. Fizika i Matematika, 2014, no. 2, 24–29  mathnet
    3. S. Zschorn, “Nonselfadjoint degenerate differential operator equations of higher order on infinite interval”, Uch. zapiski EGU, ser. Fizika i Matematika, 2014, no. 2, 39–45  mathnet
    4. Tepoyan L., Zschorn S., “Degenerate Nonselfadjoint High-Order Ordinary Differential Equations on An Infinite Interval”, J. Contemp. Math. Anal.-Armen. Aca., 50:3 (2015), 114–118  crossref  mathscinet  zmath  isi  scopus  scopus
    5. L. P. Tepoyan, “Degenerate first order differential-operator equations”, Uch. zapiski EGU, ser. Fizika i Matematika, 53:3 (2019), 163–169  mathnet
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