Publications
- Helffer, Bernard; Robert, Didier; Wang, Xue Ping.
Semiclassical analysis of a nonlinear eigenvalue problem and
nonanalytic hypoellipticity. (Russian, English)St. Petersbg. Math. J.
16, No.1, 285-296 (2004); translation from Algebra Anal. 16, No.1,
320-334 (2004).
- Robert, Didier. Nonlinear eigenvalue problems. (English)Mat. Contemp. 26, 109-127 (2004).
- Combescure, Monique; Robert, Didier. Semiclassical results in the linear response theory. (English)Ann. Phys. 305, No.1, 45-59 (2003).
- De Bièvre, Stephan; Robert, Didier. Semiclassical propagation on $|\log \hbar|$ time scales. (English) Int. Math. Res. Not. 2003, No.12, 667-696 (2003).
- Bouzouina, A.; Robert, D. Uniform
semiclassical estimates for the propagation of quantum observables.
(English) Duke Math. J. 111, No.2, 223-252 (2002).
- Combescure, M.; Robert, D. A semiclassical approach in linear response theory. (English)Weder,
Ricardo (ed.) et al., Mathematical results in quantum mechanics. A
conference on QMATH-8, Univ. Nacional Autónoma de México,
Taxco, México, December 10-14, 2001. Providence, RI: AMS,
American Mathematical Society. Contemp. Math. 307, 83-88 (2002).
- Robert, Didier. Long time propagation results in quantum mechanics. (English)
Weder, Ricardo (ed.) et al., Mathematical results in quantum mechanics.
A conference on QMATH-8, Univ. Nacional Autónoma de
México, Taxco, México, December 10-14, 2001. Providence,
RI: AMS, American Mathematical Society. Contemp. Math. 307, 255-264
(2002).
- Robert, Didier. Remarks on asymptotic solutions for time dependent Schrödinger equations. (English)
Menaldi, José Luis (ed.) et al., Optimal control and partial
differential equations. In honour of Professor Alain Bensoussan's 60th
birthday. Proceedings of the conference, Paris, France, December 4,
2000. Amsterdam: IOS Press; Tokyo: Ohmsha. 188-197 (2001).
- Combescure, Monique; Robert, Didier.
Rigorous semiclassical results for the magnetic response of an electron
gas. (English) Rev. Math. Phys. 13, No.9, 1055-1073 (2001).
- Combescure, Monique; Robert, Didier. Semiclassical results in the linear response theory. (English)
Casacuberta, Carles (ed.) et al., 3rd European congress of mathematics
(ECM), Barcelona, Spain, July 10-14, 2000. Volume II. Basel:
Birkhäuser. Prog. Math. 202, 413-420 (2001).
- Bily, J.M.; Robert, D. The semi-classical Van-Vleck formula. Application to the Aharonov-Bohm effect. (English)
Graffi, Sandro (ed.) et al., Long time behaviour of classical and
quantum systems. Proceedings of the Bologna APTEX international
conference, Bologna, Italy, September 13-17, 1999. Singapore: World
Scientific. Ser. Concr. Appl. Math. 1, 89-106 (2001).
- Bruneau, Vincent; Robert, Didier.
Asymptotics of the scattering phase for the Dirac operator: high
energy, semi-classical and non-relativistic limits. (English) Ark. Mat.
37, No.1, 1-32 (1999).
- Combescure, Monique; Ralston, James; Robert, Didier.
A proof of the Gutzwiller semiclassical trace formula using coherent
states decomposition. (English) Commun. Math. Phys. 202, No.2, 463-480
(1999).
- Robert, Didier. Semiclassical asymptotics for the spectral shift function. (English)
Buslaev, V. (ed.) et al., Differential operators and spectral theory.
M. Sh. Birman's 70th anniversary collection. Providence, RI: American
Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 187-203
(1999).
- Combescure, Monique; Robert, Didier.
A semiclassical trace formula using coherent states methods. (English.
Abridged French version)C. R. Acad. Sci., Paris, Sér. II, Fasc.
b, Méc. Phys. Astron. 326, No.9, 569-574 (1998).
- Laptev, A.; Robert, D.; Safarov, Yu.
Remarks on the paper of V. Guillemin and K. Okikiolu: ``Subprincipal
terms in Szegö estimates''. (English) Math. Res. Lett. 5, No.1-2,
57-61 (1998).
- Robert, Didier; Sordoni, Vania. Generalized determinants for Sturm-Liouville problems on the real line. (English)Greiner,
Peter C. (ed.) et al., Partial differential equations and their
applications. Lectures given at the 1995 annual seminar of the Canadian
Mathematical Society, Toronto, Canada, June 12--23, 1995. Providence,
RI: American Mathematical Society. CRM Proc. Lect. Notes. 12, 251-259
(1997).
- Combescure, M.; Robert, D.
Semiclassical spreading of quantum wave packets and applications near
unstable fixed points of the classical flow. (English) Asymptotic Anal.
14, No.4, 377-404 (1997).
- Robert, D.
Semi-classical approximation in quantum mechanics. A survey of old and
recent mathematical results. (English) Helv. Phys. Acta 71, No.1,
44-116 (1997).
- Robert, D.; Sordoni, V. Trace
formulas and Dirichlet-Neumann problems with variable boundary: The
scalar case. (English)Helv. Phys. Acta 69, No.2, 158-176 (1996).
- Combescure, Monique; Robert, Didier.Propagation
d'états cohérents par l'équation de
Schrödinger et approximation semi-classique. (Coherent states
propagation by the Schrödinger equation and semi-classical
approximation). (French. Abridged English version)C. R. Acad. Sci.,
Paris, Sér. I 323, No.8, 871-876 (1996). MSC 2000: *35Q40 81Q20
- Robert, Didier. On the Weyl formula for obstacles. (English)
Hörmander, Lars (ed.) et al., Partial differential equations and
mathematical physics. The Danish-Swedish analysis seminar, Copenhagen,
Denmark, Lund, Sweden, March 17-19, May 19-21, 1995. Proceedings.
Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 21,
264-285 (1996).
- Combescure, M.; Robert, D. Semiclassical sum rules and generalized coherent states. (English) J. Math. Phys. 36, No.12, 6596-6610 (1995).
- Combescure, Monique; Robert, Didier. Distribution of matrix
elements and level spacing for classically chaotic systems.
(English)Ann. Inst. Henri Poincaré, Phys. Théor. 61,
No.4, 443-483 (1994).
- Robert, Didier; Wang, Xue Ping. Pointwise semiclassical asymptotics for total cross sections in $N$-body problems. (English)
Ikawa, Mitsuru (ed.), Spectral and scattering theory. Proceedings of
the Taniguchi international workshop, held at Sanda, Hyogo, Japan.
Basel: Marcel Dekker. Lect. Notes Pure Appl. Math. 161, 181-196
(1994).
- Robert, Didier.
Semi-classical and high energy asymptotics of the scattering phase for
perturbations of elliptic operators. (English)Schmüdgen,
K. (ed.), Mathematical physics X. Proceedings of the 10th congress on
mathematical physics, Leipzig, Germany, July 30 - August 9, 1991.
Berlin: Springer-Verlag. 442-446 (1992).
- Robert, Didier. Relative time delay and trace formula for long range perturbations of Laplace operator. (English)Demuth,
Michael (ed.) et al., Operator calculus and spectral theory.
Proceedings of a symposium, held in Lambrecht, Germany, December 9-14,
1991. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 57,
245-253 (1992).
- Robert, Didier. A trace formula for obstacles problems and applications. (English)Demuth,
Michael (ed.) et al., Mathematical results in quantum mechanics:
International conference in Blossin (Germany), May 17-21, 1993. Basel:
Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 283-292
(1994).
- Robert, Didier.
Relative time-delay for perturbations of elliptic operators and
semiclassical asymptotics. (English)J. Funct. Anal. 126, No.1, 36-82
(1994).
- Robert, Didier.Sur
la formule de Weyl pour des ouverts non bornés. (On the Weyl
formula for unbounded open sets). (French. Abridged English version) C.
R. Acad. Sci., Paris, Sér. I 319, No.1, 29-34 (1994).
- Robert, D. On scattering theory for long range perturbations of Laplace operators. (English) J. Anal. Math. 59, 189-203 (1992).
- Robert, D.
Asymptotique de la phase de diffusion à haute énergie
pour des perturbations du second ordre du Laplacien. (Asymptotics for
high energies of the scattering phase for second order perturbations of
the Laplacian). (French)Ann. Sci. Éc. Norm. Supér., IV. Sér. 25, No.2, 107-134 (1992).
- Robert, D.(ed.) Méthodes semi-classiques, Volume 2. Colloque international (Nantes, juin 1991). (French)Astérisque.
210. Paris: Société Mathématique de France, 384 p.
FF 310.00; \$ 56.00 (2 vols.) (1992).
- Robert, D.(ed.)
Méthodes semi-classiques. Vol. 1. École
d'été (Nantes, juin 1991). (French)Astérisque.
207. Paris: Société Mathématique de France, 211 p.
FF 170.00; \$ 31.00 (1992).
- Nicoleau, François; Robert, Didier. Théorie
de la diffusion quantique pour des perturbations à longue et
courte portée du champ magnétique. (Quantum scattering
theory for long and short range perturbations of the magnetic field).
(French) Ann. Fac. Sci. Toulouse, V. Sér., Math. 12, No.2, 185-194 (1991).
- Robert, D.; Wang, Xueping.
Time-delay and spectral density for Stark Hamiltonians. II: Asymptotics
of trace formulae. (English) Chin. Ann. Math., Ser. B 12, No.3, 358-383
(1991).
- Robert, D.
High energy asymptotics for scattering phases for perturbations of
Laplace operator. (English) Integral equations and inverse problems,
Proc. Int. Conf., Varna/Bulg. 1989, Pitman Res. Notes Math. Ser. 235,
225-233 (1991).
- Robert, Didier.
Asymptotique à grande energie de la phase de diffusion pour un
potentiel. (Large energy asymptotic of the diffusion phase for a
potential.). (French) Asymptotic Anal. 3, No.4, 301-320 (1990). MSC 2000: *35P25 35P20 35J10, Reviewer: A.Martinez
- Helffer, B.; Robert, D.
Riesz means of bounded states and semi-classical limit connected with a
Lieb-Thirring conjecture. II. (English) Ann. Inst. Henri
Poincaré, Phys. Théor. 53, No.2, 139-147 (1990).
- Helffer, B.; Robert, D.
Riesz means of bound states and semiclassical limit connected with a
Lieb-Thirring's conjecture. (English) Asymptotic Anal. 3, No.2, 91-103
(1990).
- Klein, Markus; Robert, Didier; Wang, Xueping.
Breit-Wigner formula for the scattering phase in the Stark effect.
(English) Commun. Math. Phys. 131, No.1, 109-124 (1990).
- Gérard, Christian; Robert, Didier.
La limite semi-classique de la phase de Berry. (On the semi-classical
limit of Berry's phase). (French) C. R. Acad. Sci., Paris, Sér.
I 310, No.9, 677-682 (1990).
- Robert, D.Asymptotique
de la phase de diffusion à haute énergie
pour des perturbations du laplacien. (High energy asymptotics of the
scattering phase for perturbations of the Laplacian). (French)
Sémin. Équations Dériv. Partielles 1988-1989, Exp.
No.17, 14 p. (1989).
- Gérard, C.; Martinez, A.; Robert, D.
Breit-Wigner formulas for the scattering phase and the total scattering
cross-section in the semi-classical limit. (English) Commun. Math.
Phys. 121, No.2, 323-336 (1989).
- Robert, D.; Tamura, H.
Asymptotic behaviour of scattering amplitude in semi-classical limit.
(English) Partial differential equations, Proc. Symp., Holzhau/GDR
1988, Teubner- Texte Math. 112, 229-237 (1989).
- Robert, Didier; Wang, Xueping. Existence of time-delay operators for Stark-Hamiltonians. (English) Commun. Partial Differ. Equations 14, No.1, 63-98 (1989).
- Robert, D.; Tamura, H. Asymptotic
behavior of scattering amplitudes in semi-classical and low energy
limits. (English) Ann. Inst. Fourier 39, No.1, 155-192 (1989).
- Robert, D.; Tamura, H.
Limite semi-classique de l'amplitude de diffusion. (Semiclassical limit
of the diffusion amplitude). (French) Journ. Équ. Dériv.
Partielles, St.-Jean-De-Monts 1988, Exp. No.11, 9 p. (1988).
- Robert, D.; Tamura, H.
Semi-classical asymptotics for local spectral densities and time delay
problems in scattering processes. (English) J. Funct. Anal. 80, No.1,
124-147 (1988).
- Robert, Didier;Tamura, Hideo.
Semi-classical estimates for resolvents and asymptotics for total
scattering cross-sections. (English) Ann. Inst. Henri Poincaré,
Phys. Théor. 46, 415-442 (1987).
- Robert, Didier.
Analyse semi-classique de l'effet tunnel [d'après B. Helffer et
J. Sjöstrand]. (Semiclassical analysis of the tunnel effect).
(French) Sémin. Bourbaki, 38ème année, Vol.
1985/86, Exp. No.665, Astérisque 145/146, 257-281 (1987).
- Dauge, Monique; Robert, Didier.
Weyl's formula for a class of pseudodifferential operators with
negative order in $L\sp 2({\bbfR}\sp n)$. (English) Pseudo-differential
operators, Proc. Conf., Oberwolfach/Ger. 1986, Lect. Notes Math. 1256,
91-122 (1987).
- Helffer, B.; Martinez, A.; Robert, D.
Ergodicité et limite semi-classique. (Ergodicity and
semi-classical limit). (French) Commun. Math. Phys. 109, 313-326
(1987).
- Robert, Didier.
Autour de l'approximation semi-classique. (Around semiclassical
approximation). (French) Progress in Mathematics, Vol. 68.
Boston-Basel-Stuttgart: Birkhäuser. IX, 329 p.; DM 94.00
(1987).
- Robert, D.
Asymptotique semi-classique pour la densité spectrale locale
d'opérateurs de Schrödinger (d'après D. Robert et H.
Tamura). (Semi-classical asymptotics of the local spectral density of
Schrödinger operators). (French) Sémin., Équations
Dériv. Partielles 1985-1986, Exposé No.4, 11 p.
(1986).
- 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) Am. J. Math. 108, 973-1000 (1986).
- Dauge, Monique; Robert, Didier.Formule
de Weyl pour une classe d'opérateurs
pseudodifférentiels d'ordre négatif sur $L\sp
2({\bbfR}\sp n)$. (Weyl formula for a class of pseudodifferential
operators of negative order on $L\sp 2({\bbfR}\sp n))$. (French) Journ.
Équ. Dériv. Partielles, St.-Jean-De-Monts 1986, No.4, 10
p. (1986).
- Robert, Didier; Tamura, Hideo.
Asymptotique semi-classique pour la densité spectral
d'operateurs de Schrödinger et applications. (Semi-classical
symptotic for the spectral density of Schrödinger operators and
applications). (French) C. R. Acad. Sci., Paris, Sér. I 303, 35-38 (1986).
- Dauge, Monique; Robert, Didier. Formule
de Weyl pour une classe d'opérateurs pseudodifférentiels
d'ordre négatif sur $L\sp 2({\bbfR}\sp n)$. (Weyl's formula for
pseudodifferential operators of negative order in $L\sp 2({\bbfR}\sp
n))$. (French)C. R. Acad. Sci., Paris, Sér. I 302, 175-178 (1986).
- Petkov, Vesslin; Robert, Didier.
Asymptotique semi-classique du spectre d'hamiltoniens quantiques et
trajectoires classiques périodiques. (French) Commun. Partial
Differ. Equations 10, 365-390 (1985).
- 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) Am. J. Math. 106, 1199-1236 (1984).
- Robert, Didier; Tamura, Hideo.
Approximation semi-classique de la phase de diffusion pour un
potentiel. (Semi-classical approximation of the scattering phase for a
potential). (French) C. R. Acad. Sci., Paris, Sér. I 299, 89-92 (1984).
- Helffer, B.; Robert, D.
Puits de potentiel généralisés et asymptotique
semi-classique. (Generalized potential wells and semiclassical
asymptotic). (French) Ann. Inst. Henri Poincaré, Phys. Théor. 41, 291-331 (1984).
- Robert, Didier; Tamura, Hideo.
Semi-classical bounds for resolvents of Schrödinger operators and
asymptotics for scattering phases. (English) Commun. Partial Differ.
Equations 9, 1017-1058 (1984).
- Robert, Didier. Nonlinear eigenvalues problems with a small parameter. (English) Integral Equations Oper. Theory 7, 231-240 (1984).
- Robert, D.
Approximation semi-classique de la phase de diffusion pour un
potentiel. (French) Sémin. Goulaouic-Meyer-Schwartz 1983-1984,
Équat. dériv. part., Exposé No.5, 15 p.
(1984).
- Petkov, Vesselin; Robert, Didier.
Asymptotique semi-classique d'Hamiltoniens quantiques et trajectoires
classiques périodiques. (French) C. R. Acad. Sci., Paris,
Sér. I 296, 553-556 (1983).
- Robert, Didier.
Remarks on a paper of S. Zelditch: "Szegoe limit theorems in quantum
mechanics". (English) J. Funct. Anal. 53, 304-308 (1983).
- Helffer, B.; Robert, D.
Calcul fonctionnel par la transformation de Mellin et opérateurs
admissibles. (French) J. Funct. Anal. 53, 246-268 (1983).
- Helffer, B.; Robert, D.
Asymptotique des niveaux d'energie pour des Hamiltoniens à un
degré de liberte. (French) Duke Math. J. 49, 853-868
(1982).
- Robert, Didier.
Comportement asymptotique des valeurs propres d'opérateurs du
type Schrödinger à potentiel
"dégénérée". (French) J. Math. Pures Appl., IX. Sér. 61, 275-300 (1982).
- Helffer, B.; Robert, D. Comportement
semi-classique du spectre des hamiltoniens quantiques hypoelliptiques.
(French) Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 9, 405-431
(1982).
- Helffer, Bernard; Robert, Didier.
Propriétés asymptotiques du spectre d'opérateurs
pseudodifferentiels sur $R\sp n.$ (French) Commun. Partial Differ.
Equations 7, 795-882 (1982).
- Robert, Didier. Calcul fonctionnel sur les opérateurs admissibles et application. (French) J. Funct. Anal. 45, 74-94 (1982).
- Helffer, B.; Robert, D.
Comportement asymptotique precise du spectre d'opérateurs
globalement elliptiques dans $R\sp n.$ (French) Sémin.
Goulaouic-Meyer-Schwartz 1980-1981, Équat. dériv. part.,
Exposé No.2, 22 p. (1981).
- Helffer, Bernard; Robert, Didier. Comportement
asymptotique precise du spectre d'opérateurs globalement
elliptiques dans $R\sp n.$ (French) C. R. Acad. Sci., Paris,
Sér. I 292, 363-366 (1981).
- Helffer, Bernard; Robert, Didier.
Comportement semi-classique du spectre des hamiltoniens quantiques
hypoelliptiques. (French) C. R. Acad. Sci., Paris, Sér. I 292,
47-50 (1981).
- Robert, D.; Helffer, B.
Comportement semi-classique du spectre des hamiltoniens quantiques
elliptiques. (French) Ann. Inst. Fourier 31, No.3, 169-223 (1981).
- Helffer, B.; Robert, D.
Comportement semi-classique du spectre des Hamiltoniens quantiques
elliptiques. (French) Journ. Équ. Dériv. Partielles,
Saint-Jean-de-Monts 1980, Exp. No.5, 5 p. (1980).
- Pham The Lai; Robert, D. Sur un problème aux valeurs propres non linéaire. (French) Isr. J. Math. 36, 169-186 (1980).
- Pham The Lai; Robert, D.
Valeurs propres d'une classe d'équations différentielles
singulieres sur une demi-droite. (French) Ann. Sc. Norm. Super. Pisa,
Cl. Sci., IV. Ser. 6, 335-366 (1979).
- Pham The Lai; Robert, D.
Sur un problème aux valeurs propres non linéaire.
(French) Journ. Équ. Dériv. Partielles, Saint-Cast 1979,
Exp. No.15, 5 p. (1979).
- Robert, Didier.
Développement asymptotique du noyau resolvant
d'opérateurs elliptiques. (French) Osaka J. Math. 15, 233-243
(1978).
- Robert, D. Propriétés
spectrales d'opérateurs pseudo-différentiels. (French)
Commun. Partial Differ. Equations 3, 755-826 (1978).
- Lai, Pham The; Robert, Didier.
Valeurs propres d'une classe d'équations différentielles
singulieres sur une demi-droite. (French) Equat. Deriv. part., Proc.,
Saint-Jean-de-Monts 1977, Lect. Notes Math. 660, 164-171
(1978).
- Robert, D. Propriétés spectrales d'opérateurs pseudodifferentiels. (French)
Sémin. Goulaouic-Schwartz 1977-1978, Équat. dériv.
part. Anal. fonct., Exposé No.5, 10 p. (1978).
- Robert, Didier.
Sur la répartition du spectre d'opérateurs elliptiques
non autoadjoints à coefficients irréguliers. (French) Osaka J. Math. 14, 593-607 (1977).
- Robert, Didier.
Sur les opérateurs linéaires qui transforment la boule
unite d'un espace de Banach en une partie latticiellement bornee d'un
espace de Banach reticule. (French) Isr. J. Math. 22(1975), 354-360 (1976). MSC 2000: *46A40
- Robert, Didier.
Idéaux d'opérateurs sommants associés à une
fonction normante symétrique. (French) C. R. Acad. Sci., Paris,
Sér. A 278, 701-703 (1974).
- Robert, Didier.
Fonctions polynômes invariantes sur les idéaux de Schatten
minimaux. (French) C. R. Acad. Sci., Paris, Sér. A 277, 333-336
(1973).
- Robert, Didier.
Invariants orthogonaux pour certaines classes d'operateurs. (Orthogonal
invariants for certain classes of operators). (French) J. Math. Pur.
Appl., IX. Sér. 52, 81-114 (1973).
- Robert, D.
Invariants orthogonaux pour certaines classes d'opérateurs
compacts (French) C. R. Acad. Sci., Paris, Sér. A 273, 301-304
(1971).