, ? ayant rencontré les équations hypergéométriques dans notre travail, comment pouvonsnous exploiter les formes explicites de leurs solutions ?
, ? ayant rencontré les fonctions de Bessel modifiées, comment pouvons-nous exploiter l'équation différentielle qu'elles vérifient et ont-elles ici une autre signification d'un point de vue théorie des représentations ?
, ? comment exploiter la théorie des représentations pour affiner le lien mis en évidence entre les fonctions spéciales rencontrées ?
, ? comment exploiter le lien avec les équations d'Emden-Fowler ?
, Bibliographie
Irreducible Unitary Representations of the Lorentz Group, The Annals of Mathematics, vol.48, issue.3, pp.568-640, 1947. ,
DOI : 10.2307/1969129
Stability theory of differential equations. Courier Corporation, 2008. ,
On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol.45, issue.04, pp.457-468, 1991. ,
DOI : 10.1007/978-1-4684-0274-2
Semisimple groups and Riemannian symmetric spaces, 1998. ,
DOI : 10.1007/978-93-80250-92-2
representations, Duke Mathematical Journal, vol.49, issue.4, pp.869-930, 1982. ,
DOI : 10.1215/S0012-7094-82-04943-2
An introduction to the study of stellar structure, 1967. ,
Theory of Lie groups, 1946. ,
On the degenerate principal series of complex symplectic groups, Journal of Functional Analysis, vol.262, issue.9, pp.4160-4180 ,
DOI : 10.1016/j.jfa.2012.02.013
URL : https://doi.org/10.1016/j.jfa.2012.02.013
Canonical Representations of Sp (1, n ) Associated with Representations of Sp (1), Communications in Mathematical Physics, vol.202, issue.3, pp.651-667, 1999. ,
DOI : 10.1007/s002200050600
Higher transcendental functions, volume II, p.115, 1953. ,
Tables of integral transforms, volume II, 1954. ,
Analysis on Lie groups, volume 110 of Cambridge Studies in Advanced Mathematics An introduction, pp.16-45, 2008. ,
Harmonic analysis in phase space, Ann. Math. Studies, vol.122, 1989. ,
Theorie analytique de la chaleur. Paris : Chez Firmin Didot, Père et Fils, 1822 ,
DOI : 10.1017/cbo9780511693229
URL : https://babel.hathitrust.org/cgi/imgsrv/download/pdf?id=nnc1.cu50558870;orient=0;size=100;seq=11;attachment=0
Unitary representations of the Lorentz group ,
, J. Phys, vol.10, pp.93-94, 1946.
Irreducible unitary representations of locally bicompact groups, Matematicheskii Sbornik, vol.55, issue.20, pp.301-316, 1943. ,
Table of integrals, series, and products, p.115, 2007. ,
The Dual of a Parabolic Subgroup and a Degenerate Principal Series of Sp(n, C), American Journal of Mathematics, vol.93, issue.2, pp.398-428, 1971. ,
DOI : 10.2307/2373384
On quaternions ; or on a new system of imaginaries in algebra, Philosophical Magazine Series, vol.3, issue.25169, pp.489-495 ,
Orthogonal polynomials associated to a certain fourth order differential equation, The Ramanujan Journal, vol.17, issue.2, pp.295-310, 2011. ,
DOI : 10.1007/BF00046822
Special functions associated with a certain fourth-order differential equation, The Ramanujan Journal, vol.180, issue.1, pp.1-34, 2011. ,
DOI : 10.1016/S0001-8708(03)00014-8
Homogeneous Functions on Light Cones: \\the Infinitesimal Structure of some Degenerate Principal Series Representations, Bulletin of the American Mathematical Society, vol.28, issue.1, pp.1-74, 1993. ,
DOI : 10.1090/S0273-0979-1993-00360-4
Lectures on representation theory, World scientific, 1999. ,
DOI : 10.1142/3988
On the expansion of a function in terms of spherical harmonics in arbitrary dimensions, Bull. Belgian Math. Soc. Simon Stevin, vol.2, issue.4, pp.361-380, 1995. ,
Lectures on the orbit method, 2004. ,
DOI : 10.1090/gsm/064
Le programme d'Erlangen. Jacques Gabay, 1991. ,
Representation theory of semisimple groups An overview based on examples, Reprint of the 1986 original, Princeton Landmarks in Mathematics, vol.10, issue.37, pp.39-41, 2001. ,
Lie groups beyond an introduction, Progress in Mathematics . Birkhäuser Boston Inc, vol.140, issue.68, p.34, 2002. ,
DOI : 10.1007/978-1-4757-2453-0
Conformal symmetry breaking operators for differential forms on spheres, Lecture Notes in Math, vol.2170, issue.23, p.11, 2016. ,
DOI : 10.1007/978-981-10-2657-7
URL : https://hal.archives-ouvertes.fr/hal-01907092
The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p,q), Memoirs of the AMS, vol.213, issue.25, p.14, 2011. ,
An integral formula for L 2 -eigenfunctions of a fourthorder Bessel-type differential operator. Integral Transforms and Special Functions, pp.521-531, 2011. ,
Analysis on the minimal representation of O(p,q) I. Realization via conformal geometry, Advances in Mathematics, vol.180, issue.2, pp.486-512, 2003. ,
DOI : 10.1016/S0001-8708(03)00012-4
Analysis on the minimal representation of O(p,q) II. Branching laws, Advances in Mathematics, vol.180, issue.2, pp.513-550, 2003. ,
DOI : 10.1016/S0001-8708(03)00013-6
Analysis on the minimal representation of O(p,q), Advances in Mathematics, vol.180, issue.2, pp.551-595, 2003. ,
DOI : 10.1016/S0001-8708(03)00014-8
Geometric analysis on small unitary representations of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="italic">GL</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, Journal of Functional Analysis, vol.260, issue.6, pp.1682-1720, 2011. ,
DOI : 10.1016/j.jfa.2010.12.008
Differential symmetry breaking operators: I. General theory and F-method, Selecta Mathematica, vol.7, issue.2, pp.801-845, 2016. ,
DOI : 10.7146/math.scand.a-10574
URL : https://hal.archives-ouvertes.fr/hal-01907210
Special functions & their applications, Dover publications, p.114 ,
On Induced Representations of Groups, American Journal of Mathematics, vol.73, issue.3, pp.576-592, 1951. ,
DOI : 10.2307/2372309
Induced Representations of Locally Compact Groups I, The Annals of Mathematics, vol.55, issue.1, pp.101-139, 1952. ,
DOI : 10.2307/1969423
Induced Representations of Locally Compact Groups II. The Frobenius Reciprocity Theorem, The Annals of Mathematics, vol.58, issue.2, pp.193-221, 1953. ,
DOI : 10.2307/1969786
Harmonic analysis as the exploitation of symmetry-a historical survey, Bulletin of the American Mathematical Society, vol.3, issue.1, pp.543-698, 1980. ,
DOI : 10.1090/S0273-0979-1980-14783-7
Introduction à la théorie des groupes de Lie classiques . Collection Méthodes, 1986. ,
Exact solutions of the generalized Lane???Emden equations of the first and second kind, Pramana, vol.15, issue.3, pp.545-554, 2011. ,
DOI : 10.2991/jnmp.2008.15.2.3
), Journal of Mathematical Physics, vol.2, issue.20, pp.1188-1201, 1968. ,
DOI : 10.1103/RevModPhys.34.1
Solving non-linear Lane-Emden type equations using Bessel orthogonal functions collocation method. Celestial Mechanics and Dynamical Astronomy, pp.97-107 ,
Maximal degenerate representations of SL(n+1,H), J. Lie Theory, vol.9, issue.25, pp.369-382, 1999. ,
Die Vollst???ndigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Mathematische Annalen, vol.97, issue.1, pp.737-755, 1927. ,
DOI : 10.1007/BF01447892
Notes on Lie algebras. Universitext, 1990. ,
DOI : 10.1007/978-1-4613-9014-5
, Contemporary Mathematics, vol.14, issue.23, pp.285-297, 2009.
Representations of Lie groups and special functions -Volume 1 : simplest Lie groups, special functions and integral transforms, of Mathematics and Its Applications (Soviet Series, pp.11-131, 1993. ,
Representations of Lie groups and special functions -Volume 2 : class I representations, special functions and integral transforms, of Mathematics and Its Applications (Soviet Series, pp.75-76, 1993. ,
Unitary representations of reductive Lie groups, Ann. Math. Studies, vol.118, 1987. ,
Compact Lie groups and their representations, American Mathematical Soc, vol.40, issue.93, p.12, 1973. ,
DOI : 10.1090/mmono/040
, #0 %1&2 "!"%% %3"%313"4/%5% %1, pp.5-44
, %#6 6 " 16 7% 6 4" 164
6161 ,