Autovalores estáveis de uma família de operadores Autoadjuntos

Abstract

Considering that A(q) is a di erentiable family of self-adjoint operators and that M(q0) is the eigenspace associated with a certain 0 eigenvalue of A(q), with multiplicity n. We will discuss in the following project about which results we can obtain about the space of parameters the eigenvalue that are close to 0 and keep the xed multiplicity. In order to achieve the main objective of this project, we will de ne and use the transversality idea. It is an extension for higher dimensions, in which the inverse image of a regular value forms a surface. So, with the transversality idea, we can de ne when an eigenvalue is stable. Including the idea of stability, we can nd a very important and \elegant" result for the space of parameters that maintain eigenvalues close to 0 with xed multiplicity, where it will be the main theorem of this project.