On nodal sets and nodal domains on S2 and R2

Alexandre Eremenko; Dmitry Jakobson; Nikolai Nadirashvili

Journal ArticleOPEN ACCESS

On nodal sets and nodal domains on S2 and R2

Annales de l'Institut Fourier (2007) 57(7) 2345-2360

DOI: 10.5802/aif.2335

16Citations

5Readers

Abstract

We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S2. We also construct a solution of the equation δu = u in ℝ2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

Author supplied keywords

References Powered by Scopus

View more at Scopus

Cited by Powered by Scopus

View more at Scopus

Cite

CITATION STYLE

APA

Eremenko, A., Jakobson, D., & Nadirashvili, N. (2007). On nodal sets and nodal domains on S2 and R2. Annales de l’Institut Fourier, 57(7), 2345–2360. https://doi.org/10.5802/aif.2335

Readers' Seniority

PhD / Post grad / Masters / Doc 3

60%

Professor / Associate Prof. 2

40%

Readers' Discipline

Physics and Astronomy 2

40%

Computer Science 1

20%

Mathematics 1

20%

Engineering 1

20%

Article Metrics

Mentions

References: 1

View details >

On nodal sets and nodal domains on S2 and R2

Abstract

Author supplied keywords

References Powered by Scopus

Remarks on courant's nodal line theorem

Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry

On the minimum number of domains in which the nodal lines of spherical harmonics divide the sphere

Cited by Powered by Scopus

Discrete Laplace-Beltrami operators for shape analysis and segmentation

Submanifolds that are level sets of solutions to a second-order elliptic PDE

On Pleijel's nodal domain theorem

Register to see more suggestions

Cite

Readers' Seniority

Readers' Discipline

Article Metrics