Green Function and Self-adjoint Laplacians on Polyhedral Surfaces
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AbstractUsing Roelcke’s formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface$X$and compute the$S$-matrix of$X$at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian on a compact polyhedral surface of genus two with a single conical point. It turns out that the behaviour of the$S$-matrix at the zero value of the spectral parameter is sensitive to the geometry of the polyhedron.
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2006 ◽
Vol 6
(4)
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pp. 386-404
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1970 ◽
Vol 8
(13)
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pp. 1069-1071
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1971 ◽
Vol 5
(2)
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pp. 239-263
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2020 ◽
Vol 1686
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pp. 012027
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1982 ◽
Vol 383
(1785)
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pp. 313-332
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2004 ◽
Vol 16
(35)
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pp. S3695-S3702
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