IJPAM: Volume 72, No. 4 (2011)

SPECTRAL ANALYSIS OF THE SEMIGROUP ASSOCIATED
TO A MIXED FUNCTIONAL DIFFERENTIAL EQUATION

Valentina Iakovleva$^1$, Carmen Judith Vanegas$^2$
$^{1,2}$Departamento de Matemática
Universidad Simón Bolıvar
Caracas, 1080 A, VENEZUELA


Abstract. In this article we present an spectral analysis of the semigroup associated to certain mixed functional differential equation. The associated semigroup to the solution of this equation and its correspondig infinitesimal generator are defined on a closed subspace of $C^{\infty}_{[-1,1]}$. Expressions for the resolvent associated to the infinitesimal generator and its point spectrum are presented so as the analysis of the asymptotic distribution of the eigenvalues of the infinitesimal generator associated to the semigroup.

Received: July 4, 2011

AMS Subject Classification: 34J10, 34K30, 34A12

Key Words and Phrases: mixed functional differential equations, semigroups, asymptotic distribution of eigenvalues

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 4