English

On the resolvent and spectral functions of a second order differential operator with a regular singularity

Mathematical Physics 2015-06-26 v2 High Energy Physics - Theory Functional Analysis math.MP Spectral Theory Quantum Physics

Abstract

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of λ\lambda which depend on the singularity. The consequences for the pole structure of the ζ\zeta-function, and the small-tt asymptotic expansion of the heat-kernel, are also discussed.

Keywords

Cite

@article{arxiv.math-ph/0404034,
  title  = {On the resolvent and spectral functions of a second order differential operator with a regular singularity},
  author = {H. Falomir and M. A. Muschietti and P. A. G. Pisani},
  journal= {arXiv preprint arXiv:math-ph/0404034},
  year   = {2015}
}

Comments

LaTeX, 26 pages, 2 figures. Typos corrected

R2 v1 2026-07-22T16:24:19.629Z