Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 209-212
Citer cet article
M. M. Gekhtman. Asymptotics of the eigenvalues of the Dirichlet and Neumann problems for the abstract Sturm-Liouville operator. Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 209-212. http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a8/
@article{MZM_1977_21_2_a8,
author = {M. M. Gekhtman},
title = {Asymptotics of the eigenvalues of the {Dirichlet} and {Neumann} problems for the abstract {Sturm-Liouville} operator},
journal = {Matemati\v{c}eskie zametki},
pages = {209--212},
year = {1977},
volume = {21},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a8/}
}
TY - JOUR
AU - M. M. Gekhtman
TI - Asymptotics of the eigenvalues of the Dirichlet and Neumann problems for the abstract Sturm-Liouville operator
JO - Matematičeskie zametki
PY - 1977
SP - 209
EP - 212
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a8/
LA - ru
ID - MZM_1977_21_2_a8
ER -
%0 Journal Article
%A M. M. Gekhtman
%T Asymptotics of the eigenvalues of the Dirichlet and Neumann problems for the abstract Sturm-Liouville operator
%J Matematičeskie zametki
%D 1977
%P 209-212
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a8/
%G ru
%F MZM_1977_21_2_a8
Let $A>0$ be an unbounded self-adjoint operator in a Hilbert space $H$. In the Hilbert space $H_1=L_2(0,\pi;H)$ we study the spectrum of the differential equations \begin{gather*} -y''(x)+Ay=\lambda y,\quad y(0)=y(\pi)=0, \\ -y''(x)+Ay=\lambda y,\quad y'(0)=y'(\pi)=0. \end{gather*} We find the principal terms of the asymptotics of the functions $N(\lambda)$ for these problems and we ascertain the conditions under which they are asymptotically not equivalent.
