The hybrid spectral problem and Robin boundary conditions

Details The hybrid spectral problem and Robin boundary conditions The hybrid spectral problem and Robin boundary conditions

2004-09-22

arxiv.org/abs/math/0409442v4

J.Phys. A38 (2005) 4735

Mathematics

Spectral Theory

24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revision

Scientific paper

10.1088/0305-4470/38/21/017

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.

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