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Sbornik: Mathematics, 2006, Volume 197, Issue 4, Pages 525–546
DOI: https://doi.org/10.1070/SM2006v197n04ABEH003769
(Mi sm1138)
 

This article is cited in 6 scientific papers (total in 6 papers)

Deficiency indices and spectrum of self-adjoint extensions of some classes of differential operators

I. N. Dolgikha, K. A. Mirzoevb

a M. V. Lomonosov Pomor State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: Problems relating to the asymptotic behaviour in the neighbourhood of the point $+\infty$ and in the neighbourhood of the origin of a solution of an equation $l_ny=\lambda y$ of arbitrary (even or odd) order with complex-valued coefficients are studied. It is assumed here that the coefficients of the quasidifferential expression $l_n$ have the following property: if one reduces the equation $l_ny=\lambda y$ to a system of first-order differential equations, then one can transform that system to a system of differential equations with regular singular point at $x=\infty$ or $x=0$. The results obtained allow one to determine the deficiency indices of the corresponding minimal symmetric differential operators and the structure of the spectrum of self-adjoint extensions of these operators.
In addition, on the basis of refined asymptotic formulae for solutions to the equation $l_ny=\lambda y$ the deficiency numbers of a certain differential operator generated by a differential expression with leading coefficient vanishing in the interior of the interval in question are found.
Bibliography: 14 titles.
Received: 01.09.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 4, Pages 53–74
DOI: https://doi.org/10.4213/sm1138
Bibliographic databases:
UDC: 517.94
MSC: 47E05, 34L05
Language: English
Original paper language: Russian
Citation: I. N. Dolgikh, K. A. Mirzoev, “Deficiency indices and spectrum of self-adjoint extensions of some classes of differential operators”, Mat. Sb., 197:4 (2006), 53–74; Sb. Math., 197:4 (2006), 525–546
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm1138
  • https://doi.org/10.1070/SM2006v197n04ABEH003769
  • https://www.mathnet.ru/eng/sm/v197/i4/p53
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник Sbornik: Mathematics
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    Russian version PDF:314
    English version PDF:21
    References:107
    First page:2
     
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