Helffer, B.; Hoffmann-Ostenhof, T. Converse spectral problems for nodal domains. (English) Zbl 1125.35068 Mosc. Math. J. 7, No. 1, 67-84 (2007). From the abstract: “We consider two-dimensional Schrödinger operators in bounded domains. Abstractions of nodal sets are introduced and spectral conditions for them ensuring that they are actually zero sets of eigenfunctions are given. This is illustrated by an application to optimal partitions.” Reviewer: Yakov Yakubov (Tel-Aviv) Cited in 10 Documents MSC: 35P05 General topics in linear spectral theory for PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J10 Schrödinger operator, Schrödinger equation Keywords:Schrödinger operator; nodal domain; spectral theory PDFBibTeX XMLCite \textit{B. Helffer} and \textit{T. Hoffmann-Ostenhof}, Mosc. Math. J. 7, No. 1, 67--84 (2007; Zbl 1125.35068)