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Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

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Abstract

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich’s extension, the answer is easily extracted from the general result. In combination with (Bordag et al. in Commun. Math. Phys. 182(2):371–393, 1996), a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.

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Authors and Affiliations

  1. Department of Mathematics, Baylor University, Waco, TX, 76798, USA

    Klaus Kirsten

  2. Department of Mathematics, Binghamton University, Vestal Parkway East, Binghamton, NY, 13902, USA

    Paul Loya

  3. School of Mathematics, Korea Institute for Advanced Study, 207-43, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, South Korea

    Jinsung Park

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  1. Klaus Kirsten
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Kirsten, K., Loya, P. & Park, J. Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone. manuscripta math. 125, 95–126 (2008). https://doi.org/10.1007/s00229-007-0142-y

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