English

The spectral determinant for second order elliptic operators on the real line

Spectral Theory 2024-05-07 v1

Abstract

We derive an expression for the spectral determinant of a second-order elliptic differential operator T\mathcal{T} defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation Tu=0\mathcal{T} u=0. Examples of application of the resulting formula include the explicit calculation of the determinant of harmonic and anharmonic oscillators with an added bounded potential with compact support.

Keywords

Cite

@article{arxiv.2405.03469,
  title  = {The spectral determinant for second order elliptic operators on the real line},
  author = {Pedro Freitas and Jiří Lipovský},
  journal= {arXiv preprint arXiv:2405.03469},
  year   = {2024}
}

Comments

16 pages, 3 figures

R2 v1 2026-06-28T16:18:04.616Z