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Spectral determinant for the wave equation on an interval with Dirac damping (2404.11992v1)
Published 18 Apr 2024 in math.SP, math-ph, math.MP, and math.NT
Abstract: A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $\alpha$-multiple of the Dirac $\delta$-type damping, is derived. Depending on the choice of the branch cut of the logarithm used in its definition, the spectral determinant diverges either for $\alpha =2$ or $\alpha=-2$.
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