Teoria espectral para semigrupos de operadores lineares e limitados e aplicações

Abstract

In this work we discuss the spectral theory for semigroups of bounded linear operators; namely, we study the spectral theory of closed and densely defined operators in Banach spaces, semigroups of bounded linear operators, sectorial operators in Henry's sense, and fractional power theory for K-positive linear operators in Amann's sense. Furthermore, we present some applications of this theory from the study of papers: A. Cwiszewski and K. P. Rybakowski, “Dynamics of strongly damped beam equation”, Journal of Differential Equations, (2009); S. Chen and R. Triggiani, “Proof of extensions of two conjectures on structural damping for elastic systems”, Pacific J. Math., (1989); J. A. Goldstein, “Some remarks on infinitesimal generators of analytic semigroups”, Proceedings of the American Mathematical Society, (1969).