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Counting nodal lines which touch the boundary of an analytic domain
We consider the zeros on the boundary ∂Ω of a Neumann eigenfunction ϕ λj of a real analytic plane domain Ω.We prove that the number of its boundary zeros is O(λ j ) where -∆ϕ λ j = λ 2 j ϕ λ j .We also prove that the number …