Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Berard, Pierre"'
Autor:
Bérard, Pierre, Helffer, Bernard
We revisit two papers which appeared in 1999: [1] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and N. Nadirashvili. On the multiplicity of eigenvalues of the Laplacian on surfaces. Ann. Global Anal. Geom. 17 (1999) 43--48. [2] T. Hoffmann-Ostenhof, P.
Externí odkaz:
http://arxiv.org/abs/2202.06587
Autor:
Bérard, Pierre, Webb, David L.
Publikováno v:
Mathematische Zeitschrift (2021)
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For thi
Externí odkaz:
http://arxiv.org/abs/2008.12498
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022) 439-453
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions
Externí odkaz:
http://arxiv.org/abs/2007.09219
Autor:
Bérard, Pierre, Helffer, Bernard
The purpose of this note is to prove an Euler-type formula for partitions of the M\"obius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the M\"obius strip" (arXiv:2005.011
Externí odkaz:
http://arxiv.org/abs/2005.12571
Publikováno v:
Portugaliae Mathematica 78:1 (2021) 1--41
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions
Externí odkaz:
http://arxiv.org/abs/2005.01175
Publikováno v:
Journal d'analyse math\'ematique (2021)
Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first $n$ eigenfunctions has at most $n$ nodal domains. A related question is to estimate the number of connected component
Externí odkaz:
http://arxiv.org/abs/1906.03668
Autor:
Bérard, Pierre, Helffer, Bernard
Publikováno v:
Moscow Mathematical Journal 20:1 (2020) 1--25 (January-March 2020)
In the second section "Courant-Gelfand theorem" of his last published paper (Topological properties of eigenoscillations in mathematical physics, Proc. Steklov Institute Math. 273 (2011) 25--34), Arnold recounts Gelfand's strategy to prove that the z
Externí odkaz:
http://arxiv.org/abs/1807.03990
Autor:
Bérard, Pierre, Helffer, Bernard
Publikováno v:
Annales de la Facult{\'e} des Sciences de Toulouse. 30:3 (2021) 429--462
In this paper, we prove that the Extended Courant Property fails to be true for certain smooth, strictly convex domains with Neumann boundary condition: there exists a linear combination of a second and a first Neumann eigenfunctions, with three noda
Externí odkaz:
http://arxiv.org/abs/1805.01335
Autor:
Bérard, Pierre, Helffer, Bernard
Publikováno v:
n: Albeverio S., Balslev A., Weder R. (eds) Schr\"odinger Operators, Spectral Analysis and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 348. Springer, Cham. (2021)
Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first $n$ eigenfunctions has at most $n$ nodal domains. In a previous paper (Documenta Mathematica, 2018, Vol. 23, pp. 1561
Externí odkaz:
http://arxiv.org/abs/1803.00449
Autor:
Bérard, Pierre, Helffer, Bernard
Publikováno v:
Expositiones Mathematicae 38:1 (2020) 27-50
Motivated by recent questions about the extension of Courant's nodal domain theorem, we revisit a theorem published by C. Sturm in 1836, which deals with zeros of linear combination of eigenfunctions of Sturm-Liouville problems. Although well known i
Externí odkaz:
http://arxiv.org/abs/1706.08247