On nodal sets and nodal domains on S^2 and R^2

Alexandre Eremenko; Dmitry Jakobson; Nikolai Nadirashvili

arxiv: math/0611627 · v2 · pith:UCC264HWnew · submitted 2006-11-21 · 🧮 math.SP · math.AP

On nodal sets and nodal domains on S² and R²

Alexandre Eremenko , Dmitry Jakobson , Nikolai Nadirashvili This is my paper

classification 🧮 math.SP math.AP

keywords nodaldomainsequationsetsarisescomponentsconfigurationsconstruct

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S^2. We also construct a solution of the equation Delta u=u in R^2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

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On nodal sets and nodal domains on S² and R²

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