|
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
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
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
Linking options:
https://www.mathnet.ru/eng/sm1138https://doi.org/10.1070/SM2006v197n04ABEH003769 https://www.mathnet.ru/eng/sm/v197/i4/p53
|
Statistics & downloads: |
Abstract page: | 732 | Russian version PDF: | 314 | English version PDF: | 21 | References: | 107 | First page: | 2 |
|