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Mat. Sb., 2000, Volume 191, Number 11, Pages 21–46 (Mi msb521)  

On a non-local problem for irregular equations

V. V. Kornienko

A. Navoi Samarkand State University

Abstract: We study the distribution on the complex plane $\mathbb C$ of the spectrum
$$ \sigma L=P\sigma L\cup C\sigma L\cup R\sigma L $$
of the operator $L$ generated by the closure in $H=\mathscr L_2(T_1,T_2)\otimes\mathfrak H$ of an irregular operation $a(t)D_t+A$ originally defined on the smooth functions $u(t)\colon[T_1,T_2]\to\mathfrak H$ that satisfy the non-local conditions: $\mu\cdot u(T_1)-u(T_2)=0$. Here $a(t)=\sum_{k=1}^2a_k|t|^{\alpha_k}\chi_k(t)$; $a_k\in\mathbb C$, $a_k\ne 0$; $\alpha_k\in\mathbb R$; $\chi_k(t)$ is the characteristic function of the interval with end-points $0,T_k$; $-\infty<T_1<0<T_2<+\infty$; $D_t\equiv d/dt$; $A$ is a model operator acting in a Hilbert space $\mathfrak H$; $\mu\in\overline{\mathbb C}$, $\mu\ne0,\infty$.

DOI: https://doi.org/10.4213/sm521

Full text: PDF file (386 kB)
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English version:
Sbornik: Mathematics, 2000, 191:11, 1607–1633

Bibliographic databases:

UDC: 517.95
MSC: Primary 34L05; Secondary 34G10, 35M10
Received: 03.08.1999

Citation: V. V. Kornienko, “On a non-local problem for irregular equations”, Mat. Sb., 191:11 (2000), 21–46; Sb. Math., 191:11 (2000), 1607–1633

Citation in format AMSBIB
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\paper On a non-local problem for irregular equations
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\vol 191
\issue 11
\pages 21--46
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\jour Sb. Math.
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\issue 11
\pages 1607--1633
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