Dr Maurice de Gosson

Publications

[article] de Gosson, M. and Onchis, D.,
Multivariate symplectic Gabor frames with Gaussian windows
J. Fourier Anal. Appl. (2012)
[techreport] Feichtinger, H. and Onchis, D. and Wiesmeyr, C. and de, G.,
Deliverable 3.1: Optimal discretization I
(2011)
[book] de Gosson, M.,
Symplectic Methods in Harmonic Analysis and in Mathematical Physics
Symplectic Methods in Harmonic Analysis and in Mathematical Physics Pseudo-Differential Operators. Theory and Applications 7 (2011) xxiv+337 Birkhäuser/Springer Basel AG, Basel MR:MR2827662
[article] Luef, F. and de Gosson, M.,
Preferred quantization rules: Born--Jordan vs. Weyl: the pseudo-differential point of view
J. Pseudo-Differ. Oper. Appl. 2, 1 (2011) 115-139 MR:MR2781145 [pdf]
[article] Dias, C. and de Gosson, M. and Luef, F. and Prata, J.,
A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces
J. Math. Pures Appl. 96, 5 (2011) 423--445
[article] Dias, N. and de Gosson, M. and Luef, F. and Prata, J.,
A deformation quantization theory for non-commutative quantum mechanics
J. Math. Phys. 51, 7 (2010) 072101 -072112 [pdf]
[article] de Gosson, M. and Luef, F.,
Spectral and regularity properties of a Weyl calculus related to Landau quantization
Journal of Pseudo-Differential Operators and Applications 1, 1 (2010) 3-34[pdf]
[article] de Gosson, M. and Luef, F.,
On the usefulness of modulation spaces in deformation quantization
J. Phys. A: Math. Theor. 42 (2009) 315205-315221 ZBL:pre05641277 [pdf]
[article] de Gosson, M. and Luef, F.,
Symplectic capacities and the geometry of uncertainty: the irruption of symplectic topology in classical and quantum mechanics
Physics Reports 484, 5 (2009) 131-179[pdf]
[article] Piccione, P. and de Gosson, M. and De Gosson, S.,
On a product formula for the Conley-Zehnder index of symplectic paths and its applications.
Ann. Global Anal. Geom. 34, 2 (2008) 167-183 ZBL:1145.37013
[article] de Gosson, M.,
On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths
(2008)
[article] de Gosson, M.,
Spectral properties of a class of generalized Landau operators.
Commun. Partial Differ. Equations 33, 11 (September) (2008) 2096-2104 ZBL:1159.35077 [pdf]
[Article] de Gosson, M. and Luef, F.,
A new approach to the *-genvalue equation
Lett. Math. Phys. 85, 2-3 (2008) 173--183 MR:MR2443938 [pdf]
[article] de Gosson, M. and Luef, F.,
Principe d'incertitude et positivité des opérateurs à trace; applications à l'opérateur densité
Ann. Inst. H. Poincaré 9, 2 (2008) 329--346 MR:MR2399191 [pdf]
[article] de Gosson, M.,
Remarks on a paper by Cordero and Nicola on Feichtinger's Wiener amalgam spaces and the Schrödinger equation
(2007) 5 MR:- ZBL:-
[article] Isidro, J. and de Gosson, M.,
A gauge theory of quantum mechanics.
Mod. Phys. Lett. A 22, 3 (2007) 191-200 ZBL:1117.81088
[article] de Gosson, M.,
Semi-Classical propagation of wavepackets for the phase space Schrödinger equation; Interpretation in terms of the Feichtinger algebra
J. Phys. A 41, 9 (2007) 095202, 13 MR:MR2453740 [pdf]
[article] de Gosson, M.,
Metaplectic Representation, Conley-Zehnder Index, and Weyl Calculus on Phase Space
Rev. Math. Phys. (2007) ZBL:1156.81028
[article] Isidro, J. and de Gosson, M.,
A gauge theory of quantum mechanics.
Mod. Phys. Lett. A 22, 3 (2007) 191-200 ZBL:05133376
[article] Isidro, J. and de Gosson, M.,
Abelian gerbes as a gauge theory of quantum mechanics on phase space.
J. Phys. A, Math. Theor. 40, 13 (2007) 3549-3567 ZBL:05141988
[article] de Gosson, M. and Luef, F.,
Remarks on the fact that the Uncertainty Principle does not determine the Quantum State
Phys. Lett., A, 364 (2007) 453–457[pdf]
[article] de Gosson, M. and Luef, F.,
Quantum States and Hardy's Formulation of the Uncertainty Principle: a Symplectic Approach
Lett. Math. Phys. 80, 1 (2007) 69-82 MR:MR2314845 [pdf]
[article] de Gosson, M.,
Gaussian Quantum States and the Uncertainty Principle of Hardy
(2006) 1-12
[article] de Gosson, M. and de Gosson, S.,
Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators.
J. Math. Phys. 47, 12 (2006) 123506, 15 MR:MR2285155
[misc] de Gosson, M.,
Weyl calculus in phase space and the Torres-Vega and Frederick equation.
(2006) ZBL:05132417
[misc] de Gosson, M.,
Weyl calculus in phase space and the Torres-Vega and Frederick equation
(2006) ZBL:05132417
[incollection] de Gosson, M.,
Uncertainty principle, phase space ellipsoids and Weyl calculus.
Pseudo-differential Operators and related Topics Papers Based on Lectures Given at the International Conference, Växjö University, Sweden, June 22 to June 25, 2005 Boggiatto, Paolo;et al.; Operator Theory: Advances and Applications 164 (2006) 121-132 Birkhäuser; ZBL:05035715
[book] de Gosson, M.,
Symplectic Geometry and Quantum Mechanics
Operator Theory: Advances and Applications. Advances in Partial Differential Equations. 166 (2006) xx+367 Birkhäuser; ZBL:05031976
[article] de Gosson, M.,
Extended Weyl calculus and application to the phase-space Schrödinger equation.
J. Phys. A, Math. Gen. 38, 19 (2005) L325-L329 ZBL:1072.81041
[article] de Gosson, M.,
Symplectic quantum cells and Husimi-Wigner functions.
Bull. Sci. Math. 129, 3 (2005) 211-226 ZBL:1074.81050
[article] de Gosson, M.,
Symplectically covariant Schrödinger equation in phase space.
J. Phys. A, Math. Gen. 38, 42 (2005) 9263-9287 ZBL:1081.81072
[article] de Gosson, M.,
On the Weyl representation of metaplectic operators
Lett. Math. Phys. 72, 2 (2005) 129--142 MR:MR2154859
[article] de Gosson, M.,
The optimal pure Gaussian state canonically associated to a Gaussian quantum state
Phys. Lett. A 330, 3-4 (2004) 161--167 MR:MR2095989
[article] de Gosson, M.,
On the notion of phase in mechanics.
J. Phys. A, Math. Gen. 37, 29 (2004) 7297-7314 ZBL:1088.81069
[incollection] de Gosson, M. and de Gosson, S.,
The cohomological meaning of Maslov's Langrangian path intersection index.
Jean Leray '99 Conference Proceedings The Karlskrona Conference, Sweden, August 1999 in Honor of Jean Leray de Gosson, Maurice Math. Phys. Stud. 24 (2003) 143-162 Kluwer Academic Publishers; ZBL:1027.53099
[incollection] de Gosson, M.,
Semiclassical wavefunctions and Schrödinger equation.
Hyperbolic Differential Operators and related Problems et al.;Ancona, Vincenzo Lect. Notes Pure Appl. Math. 233 (2003) 287-300 Marcel Dekker; ZBL:1046.81039
[article] de Gosson, M. and de Gosson, S.,
The Maslov indices of Hamiltonian periodic orbits.
J. Phys. A, Math. Gen. 36, 48 (2003) L615-L622 ZBL:1047.37038
[article] de Gosson, M.,
Phase space quantization and the uncertainty principle.
Phys. Lett., A 317, 5-6 (2003) 365-369 ZBL:1058.81045
[incollection] de Gosson, M. and de Gosson, S.,
Symplectic path intersections and the Leray index.
Partial Differential Equations and Mathematical Physics In Memory of Jean Leray et al.;Kajitani, Kunihiko Prog. Nonlinear Differ. Equ. Appl. 52 (2003) 85-96 Birkhäuser; ZBL:1074.53068
[article] de Gosson, M.,
The symplectic camel principle and semiclassical mechanics.
J. Phys. A, Math. Gen. 35, 32 (2002) 6825-6851 ZBL:1039.53103
[book] de Gosson, M.,
The Principles of Newtonian and Quantum Mechanics. The Need for Planck's Constant, $h$.
(2001) xxii+357 Imperial College Press ZBL:0991.70001
[incollection] de Gosson, M. and Dragovich, B. and Khrennikov, A.,
Some $p$-adic differential equations.
$p$-adic Functional Analysis Proceedings of the 6th International Conference, Ioannina, Greece, July 3-7, 2000 et al.;Katsaras, A. K. Lect. Notes Pure Appl. Math. 222 (2001) 91-102 Marcel Dekker; ZBL:1006.12006
[article] de Gosson, M.,
The symplectic camel and phase space quantization.
J. Phys. A, Math. Gen. 34, 47 (2001) 10085-10096 ZBL:1008.53074
[incollection] de Gosson, M.,
Lagrangian path intersections and the Leray index.
Geometry and Topology, Aarhus Proceedings of the Conference on Geometry and Topology, Aarhus, Denmark, August 10-16, 1998 et al.;Grove, Karsten Contemp. Math. 258 (2000) 177-184 American Mathematical Society (AMS); ZBL:0985.53038
[article] de Gosson, M.,
On the classical and quantum evolution of Lagrangian half-forms in phase space.
Ann. Inst. H. Poincaré (A) Phys. théor. 70, 6 (1999) 547-573 ZBL:1049.53055
[article] de Gosson, M.,
The quantum motion of half-densities and the derivation of Schrödinger's equation.
J. Phys. A, Math. Gen. 31, 18 (1998) 4239-4247 ZBL:0961.81010
[article] de Gosson, M.,
On half-form quantization of Lagrangian manifolds and quantum mechanics in phase space.
Bull. Sci. Math. 121, 4 (1997) 301-322 ZBL:0878.58023
[book] de Gosson, M.,
Maslov Classes, Metaplectic Representation and Lagrangian Quantization.
Research Notes in Mathematics 95 (1997) 186 Wiley-VCH; ZBL:0872.58031
[article] de Gosson, M.,
On the Leray-Maslov quantization of Lagrangian submanifolds.
J. Geom. Phys. 13, 2 (1994) 158-168 ZBL:0795.58022
[article] de Gosson, M.,
Cocycles de Demazure-Kashiwara et géométrie métaplectique. (Demazure-Kashiwara cocycles and metaplectic geometry).
J. Geom. Phys. 9, 3 (1992) 255-280 ZBL:0776.53022
[article] de Gosson, M.,
The structure of $q$-symplectic geometry.
J. Math. Pures et Appl. 71 (1992) 429-453 ZBL:0829.58015
[article] de Gosson, M.,
La définition de l'indice de Maslov sans hypothèse de transversalité. (The definition of the Maslov index without a transversality assumption).
C. R. Acad. Sci. Paris, Série I 310 (1990) 279-282 ZBL:0705.22012
[article] de Gosson, M.,
La relation entre $Sp\sb{\infty}$, rev\^etement universel du groupe symplectique Sp, et Sp$\times {\bbfZ}$. (The relation between $Sp\sb{\infty}$, the universal covering of the symplectic group Sp, and Sp$\times {\bbfZ})$.
C. R. Acad. Sci. Paris, Série I 310 (1990) 245-248 ZBL:0732.22001
[article] de Gosson, M.,
Maslov indices on the metaplectic group $Mp(n)$.
Ann. Inst. Fourier 40, 3 (1990) 537-555 ZBL:0705.22013
[article] de Gosson, M.,
Microlocal regularity at the boundary for pseudo-differential operators with the transmission property. I.
Ann. Inst. Fourier 32, 3 (1982) 183-213 ZBL:0488.35080
[article] de Gosson, M.,
Paramètrix de transmission pour des opérateurs de type parabolique et application au problème de Cauchy microlocal.
C. R. Acad. Sci. Paris 292 (1981) ZBL:0484.35046
[article] de Gosson, M.,
Résultats microlocaux en hypoellipticite partielle à la frontière pour les opérateurs pseudo-différentiels de transmission.
C. R. Acad. Sci. Paris 292 (1980) ZBL:0469.35080
[article] de Gosson, M.,
Hypoellipticite partielle à la frontière des opérateurs pseudo- différentiels de transmission.
Ann. Mat. Pura Appl., IV. Ser. 123 (1980) 377-402 ZBL:0435.35087
[article] de Gosson, M.,
Remakrs on the positivity and the variation of Planck's constant
[article] Neuhauser, M. and de Gosson, M.,
On the Asymptotic Behavior of the Wigner Transform for Large Values of Planck’s Constant
[article] de Gosson, M.,
The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

Preprints

de, G. and Luef, F.,
Sub-Gaussian estimates for Wigner functions and their relation with the notion of symplectic capacity
preprint (2011)
Dias, N. and de Gosson, M. and Luef, F. and Prata, J.,
Quantum mechanics in phase space: The Schroedinger and the Moyal representations
preprint (2011) EMS
de Gosson, M. and Luef, F.,
The Pseudo-Character of the Weil representation and its relation with the Conley-Zehnder Index
preprint (2009)[pdf]
de Gosson, M. and Luef, F.,
The multi-dimensional Hardy Uncertainty Principle and its interpretation in terms of the Wigner distribution; relation with the notion of Symplectic Capacity
preprint (2008)[pdf]
de Gosson, M. and Luef, F.,
A Geometric Interpretation of Hardy's Uncertainty Principle in Terms of the Notion of Symplectic Capacity
preprint (2007)