Krein formula and S-matrix for Euclidean Surfaces with Conical Singularities

Mathematics – Spectral Theory

Scientific paper

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Accepted in Journal of Geometric Analysis

Scientific paper

We use Krein formula and the S-matrix formalism to give formulas for the
zeta-regularized determinant of non-Friedrichs extensions of the Laplacian on
Euclidean surfaces with Conical Singularities. This formula involves S(0) and
we show that the latter can be expressed using the Bergman projective
connection on the underlying Riemann surface.

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