Spectral Functions of Some Differential Operators with Singular Coefficients

H. FALOMIR

Departamento de Física, Universidad de Santiago de Chile

Workshop; Workshop on Fundamental Symmetries in High Energy Physics; 2007

Dept. Física, USACH. Organizadores: Jorge Gamboa, Mikhail Plyushchay y Fernando Méndez

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We show that the asymptotic expansion for the resolvent in the general case presents unusual powers of $\lambda$ which depend on the singularity. The consequences for the pole structure of the $\zeta$ function, and for the small-t asymptotic expansion of the heat kernel, are also discussed. A similar behavior for a system of first-order differential operators with a regular singularity is mentioned, as well as the consequences for the pole structure of the $\eta$-function (spectral asymmetry).