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arXiv · 0709.1232

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

Klaus Kirsten·Paul Loya·Jinsung Park
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Abstract

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it 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 \cite{BKD}, 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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Klaus Kirsten, Paul Loya, Jinsung Park. 2007-09-08. Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone. https://doi.org/10.1007/s00229-007-0142-y

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