manuscripta mathematica

, Volume 125, Issue 1, pp 95–126

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


DOI: 10.1007/s00229-007-0142-y

Cite this article as:
Kirsten, K., Loya, P. & Park, J. manuscripta math. (2008) 125: 95. doi:10.1007/s00229-007-0142-y


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.

Mathematics Subject Classification (2000)

Primary 58J28 58J52 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsBaylor UniversityWacoUSA
  2. 2.Department of MathematicsBinghamton UniversityBinghamtonUSA
  3. 3.School of MathematicsKorea Institute for Advanced StudyDongdaemun-gu, SeoulSouth Korea

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