Detailed asymptotic of eigenvalues on time scales

Let ={an}n{0} be a time scale with zero Minkowski (or box) dimension, where {an}n is a monotonically decreasing sequence converging to zero, and a1=1. In this paper, we find an upper bound for the eigenvalue counting function of the linear problem -u=u, with Dirichlet boundary conditions. We obtain...

Descripción completa

Detalles Bibliográficos
Autores principales: Amster, Pablo Gustavo, De Napoli, Pablo Luis, Pinasco, Juan Pablo
Publicado: 2009
Materias:
Asymptotic bounds
Asymptotic of eigenvalues
Minkowski dimension
Time scales
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10236198_v15_n3_p225_Amster
http://hdl.handle.net/20.500.12110/paper_10236198_v15_n3_p225_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10236198_v15_n3_p225_Amster
record_format dspace
spelling paper:paper_10236198_v15_n3_p225_Amster2023-06-08T16:00:10Z Detailed asymptotic of eigenvalues on time scales Amster, Pablo Gustavo De Napoli, Pablo Luis Pinasco, Juan Pablo Asymptotic bounds Asymptotic of eigenvalues Minkowski dimension Time scales Let ={an}n{0} be a time scale with zero Minkowski (or box) dimension, where {an}n is a monotonically decreasing sequence converging to zero, and a1=1. In this paper, we find an upper bound for the eigenvalue counting function of the linear problem -u=u, with Dirichlet boundary conditions. We obtain that the nth-eigenvalue is bounded below by [image omitted]. We show that the bound is optimal for the q-difference equations arising in quantum calculus. Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:De Napoli, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Pinasco, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10236198_v15_n3_p225_Amster http://hdl.handle.net/20.500.12110/paper_10236198_v15_n3_p225_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic bounds
Asymptotic of eigenvalues
Minkowski dimension
Time scales
spellingShingle Asymptotic bounds
Asymptotic of eigenvalues
Minkowski dimension
Time scales
Amster, Pablo Gustavo
De Napoli, Pablo Luis
Pinasco, Juan Pablo
Detailed asymptotic of eigenvalues on time scales
topic_facet Asymptotic bounds
Asymptotic of eigenvalues
Minkowski dimension
Time scales
description Let ={an}n{0} be a time scale with zero Minkowski (or box) dimension, where {an}n is a monotonically decreasing sequence converging to zero, and a1=1. In this paper, we find an upper bound for the eigenvalue counting function of the linear problem -u=u, with Dirichlet boundary conditions. We obtain that the nth-eigenvalue is bounded below by [image omitted]. We show that the bound is optimal for the q-difference equations arising in quantum calculus.
author Amster, Pablo Gustavo
De Napoli, Pablo Luis
Pinasco, Juan Pablo
author_facet Amster, Pablo Gustavo
De Napoli, Pablo Luis
Pinasco, Juan Pablo
author_sort Amster, Pablo Gustavo
title Detailed asymptotic of eigenvalues on time scales
title_short Detailed asymptotic of eigenvalues on time scales
title_full Detailed asymptotic of eigenvalues on time scales
title_fullStr Detailed asymptotic of eigenvalues on time scales
title_full_unstemmed Detailed asymptotic of eigenvalues on time scales
title_sort detailed asymptotic of eigenvalues on time scales
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10236198_v15_n3_p225_Amster
http://hdl.handle.net/20.500.12110/paper_10236198_v15_n3_p225_Amster
work_keys_str_mv AT amsterpablogustavo detailedasymptoticofeigenvaluesontimescales
AT denapolipabloluis detailedasymptoticofeigenvaluesontimescales
AT pinascojuanpablo detailedasymptoticofeigenvaluesontimescales
_version_ 1768546732124143616

Ejemplares similares