Valores propios asociados al operador de Hill unidimensional. Caso general.

We study Hill?s equation with general boundary conditions and white noise potential.In [3] they solve the problem with Dirichlet conditions, leaving the general case unresolved.The problem is important both from the theoretical and the applied point of view, giventhe range of applications of the sub...

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Main Authors: Cambronero, Santiago, Alfaro, Marco
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/280
http://hdl.handle.net/10669/12929
Summary: We study Hill?s equation with general boundary conditions and white noise potential.In [3] they solve the problem with Dirichlet conditions, leaving the general case unresolved.The problem is important both from the theoretical and the applied point of view, giventhe range of applications of the subject. Following [6], we give a description of thestandard brownian motion process, and mention some of its basic properties. We thenintroduce the equation to be studied, the remaining of the work being devoted to theanalysis of the asymptotic of eigenvalues.Keywords: Hill?s operator, boundary conditions, Brownian motion, eigenvalues.