Spectral functions of non-essentially self-adjoint operators

H. A. FALOMIR; P.A.G. PISANI

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2012 vol. 45 p. 4017 - 4059

1751-8113

One of the many problems to which J.S. Dowker devoted his attention is the effect of a conical singularity in the base manifold on the behavior of the quantum fields. In particular, he studied the small-t asymptotic expansion of the heat-kernel trace on a cone and its effects on physical quantities, as the Casimir energy. In this article we review some peculiar results found in the last decade, regarding the appearance of non-standard powers of t, and even negative integer powers of log(t), in this asymptotic expansion for the selfadjoint extensions of some symmetric operators with singular coefficients. Similarly, we show that the zeta-function associated to these selfadjoint extensions presents an unusual analytic structure.