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...

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Detalles Bibliográficos
Autores principales:	Amster, P., De Napoli, P., Pinasco, J.P.
Formato:	JOUR
Materias:	Asymptotic bounds Asymptotic of eigenvalues Minkowski dimension Time scales
Acceso en línea:	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

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spelling	todo:paper_10236198_v15_n3_p225_Amster2023-10-03T15:56:50Z Detailed asymptotic of eigenvalues on time scales Amster, P. De Napoli, P. Pinasco, J.P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, P. De Napoli, P. Pinasco, J.P. 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.
format	JOUR
author	Amster, P. De Napoli, P. Pinasco, J.P.
author_facet	Amster, P. De Napoli, P. Pinasco, J.P.
author_sort	Amster, P.
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
url	http://hdl.handle.net/20.500.12110/paper_10236198_v15_n3_p225_Amster
work_keys_str_mv	AT amsterp detailedasymptoticofeigenvaluesontimescales AT denapolip detailedasymptoticofeigenvaluesontimescales AT pinascojp detailedasymptoticofeigenvaluesontimescales
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Detailed asymptotic of eigenvalues on time scales

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