Geodesic
On Spectral Asymptotics of the Neumann Problem for the Sturm--Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 85-88

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

Spectral asymptotics of the Sturm–Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity property, which imposes significant restrictions on the self-similarity parameters of the weight. This work introduces a new method for estimating the eigenvalue counting function. This makes it possible to consider a much wider class of self-similar measures.
Keywords: spectral asymptotics, semi-similar measure. 
@article{FAA_2018_52_1_a10,
     author = {N. V. Rastegaev},
     title = {On {Spectral} {Asymptotics} of the {Neumann} {Problem} for the {Sturm--Liouville} {Equation} with {Arithmetically} {Self-Similar} {Weight} of a {Generalized} {Cantor} {Type}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {85--88},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a10/}
}
TY  - JOUR
AU  - N. V. Rastegaev
TI  - On Spectral Asymptotics of the Neumann Problem for the Sturm--Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2018
SP  - 85
EP  - 88
VL  - 52
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a10/
LA  - ru
ID  - FAA_2018_52_1_a10
ER  - 
%0 Journal Article
%A N. V. Rastegaev
%T On Spectral Asymptotics of the Neumann Problem for the Sturm--Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2018
%P 85-88
%V 52
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a10/
%G ru
%F FAA_2018_52_1_a10
N. V. Rastegaev. On Spectral Asymptotics of the Neumann Problem for the Sturm--Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 85-88. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a10/