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math.AP2022
Upper bounds on eigenvalue multiplicities for spheres and plane domains revisited
Pierre Bérard, Bernard Helffer
We revisit two papers which appeared in 1999: M.~Hoffmann-Ostenhof, T.~Hoffmann-Ostenhof, and N.~Nadirashvili [Ann. Global Anal. Geom. 17 (1999) 43--48] and T.~Hoff\-mann-Ostenhof,…
math.AP2017★ 6 cited
On Courant's nodal domain property for linear combinations of eigenfunctions, Part I
Pierre Bérard, Bernard Helffer
According to Courant's theorem, an eigenfunction as\-sociated with the -th eigenvalue has at most nodal domains. A footnote in the book of Courant and Hilbert, states…