Operators arising as Second Variation of optimal control problems and their spectral asymptotics

Abstract

We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this family in terms of a set of finite dimensional data and we apply this results to a particular class of singular extremal to get a nice description of the spectrum of the second variation.

arXiv comment34 pages, new and improved exposition and many typos corrected