Daudé, Thierry; Helffer, Bernard; Nicoleau, François Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon. (English. French summary) Zbl 07755373 Ann. Math. Qué. 47, No. 2, 295-330 (2023). Reviewer: Denis Borisov (Ufa) MSC: 35P15 58J50 35J25 PDFBibTeX XMLCite \textit{T. Daudé} et al., Ann. Math. Qué. 47, No. 2, 295--330 (2023; Zbl 07755373) Full Text: DOI arXiv
Bérard, Pierre; Helffer, Bernard Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains application to the extended Courant property. (English. French summary) Zbl 1479.35581 Ann. Fac. Sci. Toulouse, Math. (6) 30, No. 3, 429-462 (2021). MSC: 35P05 35J25 58J50 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Ann. Fac. Sci. Toulouse, Math. (6) 30, No. 3, 429--462 (2021; Zbl 1479.35581) Full Text: DOI arXiv
Bérard, Pierre; Helffer, Bernard On Courant’s nodal domain property for linear combinations of eigenfunctions. II. (English) Zbl 1472.35250 Albeverio, Sergio (ed.) et al., Schrödinger operators, spectral analysis and number theory. In memory of Erik Balslev. Cham: Springer. Springer Proc. Math. Stat. 348, 47-88 (2021). MSC: 35P05 35J25 58J50 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Springer Proc. Math. Stat. 348, 47--88 (2021; Zbl 1472.35250) Full Text: DOI arXiv
Bérard, Pierre; Helffer, Bernard Sturm’s theorem on the zeros of sums of eigenfunctions: Gelfand’s strategy implemented. (English) Zbl 1472.34004 Mosc. Math. J. 20, No. 1, 1-25 (2020). Reviewer: Manfred Möller (Johannesburg) MSC: 34-02 34B24 34L10 34C10 35P99 58J50 34-03 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Mosc. Math. J. 20, No. 1, 1--25 (2020; Zbl 1472.34004) Full Text: arXiv Link
Gittins, K.; Helffer, B. Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter. (English. French summary) Zbl 1434.35025 Ann. Math. Qué. 44, No. 1, 91-123 (2020). MSC: 35P05 35J05 58J50 58J37 PDFBibTeX XMLCite \textit{K. Gittins} and \textit{B. Helffer}, Ann. Math. Qué. 44, No. 1, 91--123 (2020; Zbl 1434.35025) Full Text: DOI arXiv
Gittins, Katie; Helffer, Bernard Courant-sharp Robin eigenvalues for the square and other planar domains. (English) Zbl 1444.35118 Port. Math. (N.S.) 76, No. 1, 57-100 (2019). Reviewer: James Bernard Kennedy (Lisboa) MSC: 35P05 35J05 35J25 58J50 PDFBibTeX XMLCite \textit{K. Gittins} and \textit{B. Helffer}, Port. Math. (N.S.) 76, No. 1, 57--100 (2019; Zbl 1444.35118) Full Text: DOI arXiv
Bérard, Pierre H.; Helffer, Bernard On Courant’s nodal domain property for linear combinations of eigenfunctions. I. (English) Zbl 1403.35192 Doc. Math. 23, 1561-1585 (2018). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 35P99 35Q99 58J50 PDFBibTeX XMLCite \textit{P. H. Bérard} and \textit{B. Helffer}, Doc. Math. 23, 1561--1585 (2018; Zbl 1403.35192) Full Text: DOI arXiv
Bérard, Pierre; Helffer, Bernard Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in \(\mathbb{R}^2\). (English) Zbl 1391.35020 Girouard, Alexandre (ed.) et al., Geometric and computational spectral theory. Lectures from the Séminaire de Mathématiques Supérieures, Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada, June 15–26, 2015. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-2665-1/pbk; 978-1-4704-4258-3/ebook). Contemporary Mathematics 700. Centre de Recherches Mathématiques Proceedings, 87-116 (2017). MSC: 35B05 35Q40 58J50 81Q05 35P05 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Contemp. Math. 700, 87--116 (2017; Zbl 1391.35020) Full Text: DOI arXiv Link
Bérard, Pierre; Helffer, Bernard Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle. (English) Zbl 1382.58021 Lett. Math. Phys. 106, No. 12, 1729-1789 (2016). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 35B05 35P20 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Lett. Math. Phys. 106, No. 12, 1729--1789 (2016; Zbl 1382.58021) Full Text: DOI arXiv
Helffer, Bernard; Sundqvist, Mikael Persson On nodal domains in Euclidean balls. (English) Zbl 1362.35200 Proc. Am. Math. Soc. 144, No. 11, 4777-4791 (2016). Reviewer: Daniel Beltiţă (Bucureşti) MSC: 35P20 35B05 58J50 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{M. P. Sundqvist}, Proc. Am. Math. Soc. 144, No. 11, 4777--4791 (2016; Zbl 1362.35200) Full Text: DOI arXiv HAL
Bérard, P.; Helffer, B. A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited. (English) Zbl 1351.33014 Monatsh. Math. 180, No. 3, 435-468 (2016). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C55 35B05 58J50 35P20 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Monatsh. Math. 180, No. 3, 435--468 (2016; Zbl 1351.33014) Full Text: DOI arXiv
Helffer, Bernard; Sundqvist, Mikael Persson Nodal domains in the square – the Neumann case. (English) Zbl 1342.35198 Mosc. Math. J. 15, No. 3, 455-495 (2015). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 35P20 35B05 58J50 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{M. P. Sundqvist}, Mosc. Math. J. 15, No. 3, 455--495 (2015; Zbl 1342.35198) Full Text: arXiv Link
Bérard, Pierre; Helffer, Bernard Dirichlet eigenfunctions of the square membrane: Courant’s property, and A. Stern’s and Å. Pleijel’s analyses. (English) Zbl 1390.35209 Baklouti, Ali (ed.) et al., Analysis and geometry. MIMS-GGTM, Tunis, Tunisia, March 24–27, 2014. Proceedings of the international conference. In honour of Mohammed Salah Baouendi. Cham: Springer (ISBN 978-3-319-17442-6/hbk; 978-3-319-17443-3/ebook). Springer Proceedings in Mathematics & Statistics 127, 69-114 (2015). MSC: 35P20 35B05 58J50 PDFBibTeX XMLCite \textit{P. Bérard} and \textit{B. Helffer}, Springer Proc. Math. Stat. 127, 69--114 (2015; Zbl 1390.35209) Full Text: DOI arXiv
Helffer, B. Introduction to some conjectures for spectral minimal partitions. (English) Zbl 1247.35181 J. Egypt. Math. Soc. 19, No. 1-2, 45-51 (2011). MSC: 35R01 35P05 58J50 58J05 PDFBibTeX XMLCite \textit{B. Helffer}, J. Egypt. Math. Soc. 19, No. 1--2, 45--51 (2011; Zbl 1247.35181) Full Text: DOI
Helffer, Bernard; Kordyukov, Yuri A. Semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator: the case of discrete wells. (English) Zbl 1218.58017 Braverman, Maxim (ed.) et al., Spectral theory and geometric analysis. International conference in honor of Mikhail Shubin’s 65th birthday, Northeastern University, Boston, MA, USA, July 29–August 2, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4948-4/pbk). Contemporary Mathematics 535, 55-78 (2011). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J37 58J50 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{Y. A. Kordyukov}, Contemp. Math. 535, 55--78 (2011; Zbl 1218.58017) Full Text: arXiv
Helffer, Bernard; Hoffmann-Ostenhof, Thomas; Terracini, Susanna On spectral minimal partitions: the case of the sphere. (English) Zbl 1230.35072 Laptev, Ari (ed.), Around the research of Vladimir Maz’ya. III. Analysis and applications. Dordrecht: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-1-4419-1344-9/hbk; 978-1-4419-1345-6/ebook; 978-5-9018-7343-4/hbk). International Mathematical Series (New York) 13, 153-178 (2010). MSC: 35P05 47F05 58J50 PDFBibTeX XMLCite \textit{B. Helffer} et al., Int. Math. Ser., N.Y. 13, 153--178 (2010; Zbl 1230.35072) Full Text: DOI arXiv
Helffer, B.; Kordyukov, Y. A. Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: analysis near the bottom. (English) Zbl 1184.35233 J. Funct. Anal. 257, No. 10, 3043-3081 (2009). Reviewer: Michael Perelmuter (Kyïv) MSC: 35P15 35J10 58J05 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{Y. A. Kordyukov}, J. Funct. Anal. 257, No. 10, 3043--3081 (2009; Zbl 1184.35233) Full Text: DOI arXiv
Kordyukov, Yu. A.; Helffer, B. Periodic magnetic Schrödinger operators: spectral gaps and tunneling effect. (English. Russian original) Zbl 1237.58029 Proc. Steklov Inst. Math. 261, 171-182 (2008); translation from Tr. Mat. Inst. Steklova 261, 176-187 (2008). MSC: 58J60 35J10 35B10 35P05 35R01 47F05 PDFBibTeX XMLCite \textit{Yu. A. Kordyukov} and \textit{B. Helffer}, Proc. Steklov Inst. Math. 261, 171--182 (2008; Zbl 1237.58029); translation from Tr. Mat. Inst. Steklova 261, 176--187 (2008) Full Text: DOI arXiv
Helffer, Bernard; Kordyukov, Yuri A. Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells. (English) Zbl 1131.35054 Trans. Am. Math. Soc. 360, No. 3, 1681-1694 (2008). Reviewer: Themistocles M. Rassias (Athens) MSC: 35P20 35J10 47F05 58J50 81Q10 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{Y. A. Kordyukov}, Trans. Am. Math. Soc. 360, No. 3, 1681--1694 (2008; Zbl 1131.35054) Full Text: DOI arXiv
Nier, F.; Helffer, B. Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary. (English) Zbl 1108.58018 Mém. Soc. Math. Fr., Nouv. Sér. 105, 89 p. (2006). Reviewer: Alberto Parmeggiani (Bologna) MSC: 58J10 58J32 58K65 60J60 81Q10 81Q20 PDFBibTeX XMLCite \textit{F. Nier} and \textit{B. Helffer}, Mém. Soc. Math. Fr., Nouv. Sér. 105, 89 p. (2006; Zbl 1108.58018)
Helffer, Bernard; Klein, Markus; Nier, Francis Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach. (English) Zbl 1079.58025 Mat. Contemp. 26, 41-85 (2004). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 58J10 35J05 58J37 35P15 PDFBibTeX XMLCite \textit{B. Helffer} et al., Mat. Contemp. 26, 41--85 (2004; Zbl 1079.58025)
Helffer, Bernard; Nier, Francis Criteria to the Poincaré inequality associated with Dirichlet forms in \(\mathbb{R}^d,\,d\geq 2\). (English) Zbl 1098.31005 Int. Math. Res. Not. 2003, No. 22, 1199-1223 (2003). MSC: 31C25 35P05 47D07 58J50 35J20 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{F. Nier}, Int. Math. Res. Not. 2003, No. 22, 1199--1223 (2003; Zbl 1098.31005) Full Text: DOI
Helffer, Bernard Semiclassical analysis, Witten Laplacians, and statistical mechanics. (English) Zbl 1046.82001 Series on Partial Differential Equations and Applications 1. Singapore: World Scientific (ISBN 981-238-098-1/hbk). ix, 179 p. (2002). Reviewer: Mircea Puta (Timişoara) MSC: 82-02 82B10 58J37 58J50 81Q20 PDFBibTeX XMLCite \textit{B. Helffer}, Semiclassical analysis, Witten Laplacians, and statistical mechanics. Singapore: World Scientific (2002; Zbl 1046.82001)
Helffer, Bernard; Mohamed, Arbderemane Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells. (English) Zbl 0851.58046 J. Funct. Anal. 138, No. 1, 40-81 (1996). Reviewer: M.Biroli (Monza) MSC: 58J50 35P05 58Z05 82D40 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{A. Mohamed}, J. Funct. Anal. 138, No. 1, 40--81 (1996; Zbl 0851.58046) Full Text: DOI Link
Helffer, B. Formes normales pour des opérateurs pseudodifférentiels semiclassiques en dimension 1. (Normal forms for semiclassical pseudodifferential operators of dimension 1). (French) Zbl 0699.35273 Sémin., Équations Dériv. Partielles 1988-1989, Exp. No. 2, 12 p. (1989). Reviewer: L.Rodino MSC: 35S05 58J40 PDFBibTeX XML Full Text: Numdam EuDML
Helffer, B.; Sjöstrand, J. A proof of the Bott inequalities. (English) Zbl 0693.58019 Algebraic analysis, Pap. Dedicated to Prof. Mikio Sato on the Occas. of his Sixtieth Birthday, Vol. 1, 171-183 (1989). Reviewer: J.Marschall MSC: 58J10 35J99 PDFBibTeX XML
Sjöstrand, J.; Helffer, B. Semiclassical analysis for Harper’s equation. (English) Zbl 0759.47022 Recent developments in hyperbolic equations, Proc. Conf., Pisa/Italy 1987, Pitman Res. Notes Math. Ser. 183, 312-321 (1988). MSC: 47B39 47B37 47A10 58J50 81Q20 PDFBibTeX XMLCite \textit{J. Sjöstrand} and \textit{B. Helffer}, in: Bilinear symbolic calculus and controlled interaction in nonlinear strictly hyperbolic equations. . 312--321 (1988; Zbl 0759.47022)
Helffer, B.; Sjöstrand, J. Puits multiples en mécanique semi-classique. V: Étude des minipuits. (Multiple wells in semi-classical mechanics. V: Study of miniwells). (French) Zbl 0628.35024 Current topics in partial differential equations, Pap. dedic. S. Mizohata Occas. 60th Birthday, 133-186 (1986). Reviewer: N.Jacob MSC: 35J10 58J50 35P25 PDFBibTeX XML
Helffer, B.; Robert, D. Étude du spectre pour un opérateur globalement elliptique dont le symbole de Weyl présente des symétries. II: Action des groupes de Lie compacts. (Spectral study for a globally elliptic operator the Weyl symbol of which presents symmetries. II: Actions of compact Lie groups). (French) Zbl 0605.58042 Am. J. Math. 108, 973-1000 (1986). Reviewer: M.Puta MSC: 58J50 58J70 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{D. Robert}, Am. J. Math. 108, 973--1000 (1986; Zbl 0605.58042) Full Text: DOI
Helffer, B.; Sjöstrand, J. Puits multiples en mécanique semi-classique. IV: Étude du complexe de Witten. (Multiple wells in semi-classical limit. IV: Investigation of the Witten complex). (French) Zbl 0597.35024 Commun. Partial Differ. Equations 10, 245-340 (1985). Reviewer: J.Chrastina MSC: 35J10 58J50 58E05 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{J. Sjöstrand}, Commun. Partial Differ. Equations 10, 245--340 (1985; Zbl 0597.35024) Full Text: DOI
Helffer, B.; Sjöstrand, J. Puits multiples en limite semi-classique. II: Interaction moléculaire. Symétries. Perturbation. (Multiple wells in the semi-classical limit. II: Molecular interaction. Symmetry. Perturbation). (French) Zbl 0595.35031 Ann. Inst. Henri Poincaré, Phys. Théor. 42, 127-212 (1985). Reviewer: J.Chrastina MSC: 35J10 58J32 35P15 35P99 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{J. Sjöstrand}, Ann. Inst. Henri Poincaré, Phys. Théor. 42, 127--212 (1985; Zbl 0595.35031) Full Text: Numdam EuDML
Helffer, Bernard; Robert, Didier Étude du spectre pour un opérateur globalement elliptique dont le symbole de Weyl présente des symétries. I: Action des groupes finis. (Study of the spectrum of a global elliptic operator whose Weyl symbol shows symmetries. I: Action of finite groups). (French) Zbl 0583.58029 Am. J. Math. 106, 1199-1236 (1984). Reviewer: J.Marschall MSC: 58J50 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{D. Robert}, Am. J. Math. 106, 1199--1236 (1984; Zbl 0583.58029) Full Text: DOI
Helffer, B.; Nourrigat, J. Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. (French) Zbl 0549.35026 Rend. Sem. Mat., Torino, Fasc. Spec., Linear partial and pseudo-differential operators, Conv. Torino/Italy 1982, 115-134 (1983). MSC: 35H10 58J40 PDFBibTeX XML
Helffer, B.; Nourrigat, J. Hypoellipticite maximale pour des opérateurs polynômes de champs de vecteurs. (French) Zbl 0454.58019 Journ. Équ. Dériv. Partielles, Saint-Jean-de-Monts 1980, Exp. No. 2, 2 p. (1980). MSC: 58J99 58J10 PDFBibTeX XML Full Text: Numdam EuDML
Helffer, B.; Mattera, Cl. Analyticite et iterés reduits d’un système de champs de vecteurs. (French) Zbl 0452.35123 Commun. Partial Differ. Equations 5, 1065-1072 (1980). MSC: 35S99 58J47 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{Cl. Mattera}, Commun. Partial Differ. Equations 5, 1065--1072 (1980; Zbl 0452.35123) Full Text: DOI
Helffer, B.; Nourrigat, J. Opérateurs différentiels hypoelliptiques et groupes nilpotents. (French) Zbl 0411.35028 Sémin. Goulaouic-Schwartz 1978-1979, Équat. dériv. part. Exposé No. 5, 16 p. (1979). MSC: 35H10 58J40 PDFBibTeX XML Full Text: Numdam EuDML
Helffer, B. Hypoellipticite pour des opérateurs différentiels sur des groupes de Lie nilpotents. (French) Zbl 0464.58017 Pseudodifferential operators with applications, C.I.M.E., Bressanone 1977, 73-88 (1978). MSC: 58J40 22E27 43A85 PDFBibTeX XML
[Helffer, Bernard; Ezin, Jean-Pierre; Gallot, Sylvain; Polombo, Albert; Bérard Bergery, Lionel; Averous, Genevieve; Deschamps, Annie; Calabi, Eugenio; Bourguignon, Jean-Pierre; Yau, Shing-Tung] Première classe de Chern et courbure de Ricci: preuve de la conjecture de Calabi (Séminaire Palaiseau, France, March–June 1978). (French) Zbl 0397.35028 Astérisque 58. Paris: Société Mathématique de France. 169 p. (1978). MSC: 35J99 53C55 58J60 PDFBibTeX XML
Helffer, Bernard; Nourrigat, Jean Hypoellipticite pour des opérateurs sur des groupes de Lie nilpotents. (French) Zbl 0387.35021 C. R. Acad. Sci., Paris, Sér. A 287, 395-398 (1978). MSC: 35H10 58J99 22E25 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{J. Nourrigat}, C. R. Acad. Sci., Paris, Sér. A 287, 395--398 (1978; Zbl 0387.35021)
Helffer, B.; Rodino, L. Opérateurs différentiels ordinaires intervenant dans l’étude de l’hypoellipticite. (French) Zbl 0358.58011 Boll. Unione Mat. Ital., V. Ser., B 14, 491-522 (1977). MSC: 58J40 65H10 PDFBibTeX XMLCite \textit{B. Helffer} and \textit{L. Rodino}, Boll. Unione Mat. Ital., V. Ser., B 14, 491--522 (1977; Zbl 0358.58011)
Helffer, B. Sur une classe d’opérateurs pseudodifferentiels hypoelliptiques à caractéristiques doubles, d’après L. Hörmander. (French) Zbl 0306.35033 Sémin. Goulaouic-Lions-Schwartz 1974-1975, Équat. dériv. part. lin. non-lin., Exposé XXII, 17 p. (1975). MSC: 35H10 35S05 58J40 PDFBibTeX XML Full Text: Numdam EuDML