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The Point Spectrum of Smooth Noncompact Hyperbolic Surfaces with Finite Area

Richard Ninness
Dec 2022
摘要
We construct a sequence of boundary value problems on compact subsets ofsmooth noncompact hyperbolic surfaces of finite area. We prove that thesesquilinear forms associated to these boundary value problems are stable aswell as consistent at continuous functions which vanish at cusps. We also givenan explicit form for the symbol expansion of the Dirichlet-to-Neumann operatorof a certain Schrodinger operator. The symbols appearing in the expansion ofthis Dirichlet-to-Neumann operator can be calculated quickly by a computerusing the formulas we provide in this paper.
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