2007/01/01 by Alexandre Erëmenko, Dmitry Jakobson, Nikolaï Nadirashvili · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Nonlinear Partial Differential Equations #NODAL #Eigenfunction #Modified nodal analysis #Spherical harmonics #Nodal analysis #Mathematics #Cardinal point #Harmonics #Physics #Mathematical analysis #Topology (electrical circuits) #Mathematical physics #Combinatorics #Eigenvalues and eigenvectors #Quantum mechanics #Optics
paper · pdf · doi:10.5802/aif.2335
openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . We also construct a solution of the equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>u</mml:mi> </mml:mrow> </mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>ℝ</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.