Livres, Actes et Séminaires du Centre Mersenne

[1] V.I Arnold Topological properties of eigenoscillations in mathematical physics, Proceedings of the Steklov Institute of Mathematics, Volume 273 (2011), pp. 25-34 | MR | Zbl

[2] R. Band; M. Bersudsky; D. Fajman A note on Courant sharp eigenvalues of the Neumann right-angled isosceles triangle (2015) (https://arxiv.org/abs/1507.03410v1)

[3] R. Band; M. Bersudsky; D. Fajman Courant-sharp eigenvalues of Neumann $2$-rep-tiles (2016) (https://arxiv.org/abs/1507.03410v2) | MR

[4] P. Bérard; B. Helffer Partial edited extracts from Antonie Stern’s thesis, Séminaire de Théorie Spectrale et Géométrie, Volume 32, Institut Fourier, 2014-2015

[5] P. Bérard; B. Helffer Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle (2015) (https://arxiv.org/abs/1503.00117, To appear in Letters in Mathematical Physics)

[6] P. Bérard; B. Helffer; Ali Baklouti; Aziz El Kacimi; Sadok Kallel; Nordine Mir Dirichlet eigenfunctions of the square membrane: Courant’s property, and A. Stern’s and Å. Pleijel’s analyses, Analysis and Geometry. MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi (Springer Proceedings in Mathematics & Statistics), Volume 127 (2015), pp. 69-114 | MR

[7] P. Bérard; B. Helffer On the nodal patterns of the 2D isotropic quantum harmonic oscillator (2015) (https://arxiv.org/abs/1506.02374)

[8] P. Bérard; B. Helffer A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited, Monatshefte für Mathematik, Volume 180 (2016), pp. 435-468 | DOI | MR

[9] L. Bérard Bergery; J.P. Bourguignon Laplacians and submersions with totally geodesic fibers, Illinois Journal of Mathematics, Volume 26 (1982), pp. 181-200 | MR | Zbl

[10] V. Bonnaillie-Noël; B. Helffer Nodal and spectral minimal partitions, The state of the art in 2015 (2015) https://arxiv.org/abs/1506.07249, To appear in the book “Shape optimization and spectral theory”. A. Henrot Ed. (De Gruyter Open)

[11] P. Charron On Pleijel’s theorem for the isotropic harmonic oscillator, Université de Montréal (2015) (Masters thesis)

[12] P. Charron A Pleijel type theorem for the quantum harmonic oscillator (2015) (https://arxiv.org/abs/1512.07880, To appear in J. Spectral Theory)

[13] P. Charron; B. Helffer; T. Hoffmann-Ostenhof Pleijel’s theorem for Schrödinger operators with radial potentials (2016) (https://arxiv.org/abs/1604.08372)

[14] S.Y Cheng Eigenfunctions and nodal sets, Commentarii Mathematici Helvetici, Volume 51 (1976), pp. 43-55 | MR | Zbl

[15] R. Courant Ein allgemeiner Satz zur Theorie der Eigenfunktionen selbstadjungierter Differentialausdrücke, Nachr. Ges. Göttingen (1923), pp. 81-84

[16] R. Courant; D. Hilbert Methods of Mathematical Physics, 1, Wiley-VCH Verlag GmbH & Co. KGaA. New York, 1953 | Zbl

[17] R. Courant; D. Hilbert Methoden der Mathematischen Physik, Heidelberger Taschenbücher Band 30, I, Springer, 1968 (Dritte Auflage) | MR | Zbl

[18] A. Eremenko; D. Jakobson; N. Nadirashvili On nodal sets and nodal domains on ${𝕊}^2$, Annales Institut Fourier, Volume 57 (2007), pp. 2345-2360 | Numdam | MR | Zbl

[19] G. Gauthier-Shalom; K. Przybytkowski Description of a nodal set on ${𝕋}^2$ (2006) Research report (unpublished)

[20] B. Helffer; T. Hoffmann-Ostenhof Minimal partitions for anisotropic tori, Journal of Spectral Theory, Volume 4 (2014), pp. 221-233 | MR

[21] B. Helffer; M. Persson Sundqvist Nodal domains in the square – The Neumann case, Moscow Mathematical Journal, Volume 15 (2015), pp. 455-495 | MR

[22] B. Helffer; M. Persson Sundqvist On nodal domains in Euclidean balls, Proceeding of the American Mathematical Society, Volume 144 (2016), pp. 4777-4791 | MR

[23] D. Jakobson; N. Nadirashvili Eigenvalues with few critical points, Journal of Differential Geometry, Volume 53 (1999), pp. 177-182 | MR | Zbl

[24] N. Kuznetsov On delusive nodal sets of free oscillations, European Mathematical Society Newsletter, Volume 96 (2015), pp. 34-40 | MR

[25] C. Léna Courant-sharp eigenvalues of a two-dimensional torus, C. R. Math. Acad. Sci. Paris, Volume 353 (2015) no. 6, pp. 535-539 (doi:10.1016/j.crma.2015.03.014) | MR

[26] C. Léna On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori (2015) (https://arxiv.org/abs/1504.03944)

[27] C. Léna Pleijel’s nodal domain theorem for Neumann eigenfunctions (2016) (https://arxiv.org/abs/1609.02331)

[28] H. Lewy On the minimum number of domains in which the nodal lines of spherical harmonics divide the sphere, Communications in Partial Differential Equations, Volume 12 (1977), pp. 1233-1244 | MR | Zbl

[29] J. Leydold Knotenlinien und Knotengebiete von Eigenfunktionen, Universität Wien (1989) Diplom Arbeit (unpublished)

[30] J. Leydold On the number of nodal domains of spherical harmonics, Topology, Volume 35 (1996), pp. 301-321 | MR | Zbl

[31] Å. Pleijel Remarks on Courant’s nodal theorem, Communications in Pure and Applied Mathematics, Volume 9 (1956), pp. 543-550 | MR | Zbl

[32] F. Pockels Über die partielle Differentialgleichung $\Delta u+k^{2}u=0$ und deren Auftreten in mathematischen Physik, Teubner- Leipzig, 1891 (Historical Math. Monographs. Cornell University http://ebooks.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=00880001)

[33] A. Stern Bemerkungen über asymptotisches Verhalten von Eigenwerten und Eigenfunktionen, Druck der Dieterichschen Universitäts-Buchdruckerei (W. Fr. Kaestner), Göttingen, Germany (1925) (Ph. D. Thesis)

[34] C. Sturm Mémoire sur les équations différentielles linéaires du second ordre, Journal de Mathématiques Pures et Appliquées, Volume 1 (1836), p. 106-186, 269-277, 375-444 | EuDML

[35] A. Vogt Wissenschaftlerinnen in Kaiser-Wilhelm-Instituten. A-Z, Veröffentlichungen aus dem Archiv der Max-Planck-Gesellschaft, 12, Archiv der Max-Planck-Gesellschaft, 2008