Geodesic
The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential
Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 1-43

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is concerned with the spectral properties of second-order differential operators defined by periodic and quasi-periodic boundary conditions. We obtain asymptotic formulae for the eigenvalues, derive estimates of projections, give estimates for the equiconvergence of spectral decompositions, find sufficient conditions for operators to be spectral, and write down an asymptotic expansion for the semigroup of operators generated by the negative of the differential operator under consideration. Our estimates involve coefficients of the Fourier potential. The main results of the paper are obtained by using the method of similar operators. Bibliography: 34 titles.
Keywords: spectrum of an operator, method of similar operators, Hill's differential operator, asymptotic behaviour of eigenvalues, semigroup of operators. 
@article{SM_2017_208_1_a0,
     author = {A. G. Baskakov and D. M. Polyakov},
     title = {The method of similar operators in the spectral analysis of the {Hill} operator with nonsmooth potential},
     journal = {Sbornik. Mathematics},
     pages = {1--43},
     publisher = {mathdoc},
     volume = {208},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_1_a0/}
}
TY  - JOUR
AU  - A. G. Baskakov
AU  - D. M. Polyakov
TI  - The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1
EP  - 43
VL  - 208
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_1_a0/
LA  - en
ID  - SM_2017_208_1_a0
ER  - 
%0 Journal Article
%A A. G. Baskakov
%A D. M. Polyakov
%T The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential
%J Sbornik. Mathematics
%D 2017
%P 1-43
%V 208
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2017_208_1_a0/
%G en
%F SM_2017_208_1_a0
A. G. Baskakov; D. M. Polyakov. The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential. Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 1-43. http://geodesic.mathdoc.fr/item/SM_2017_208_1_a0/