Representations of groups in solution spaces of invariant differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 489-499 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present different versions of the definition of invariant differential equations and introduce the notion of a spectrum for these equations. We give examples of an explicit description of the spectrum and introduce sufficient conditions for discreteness of the spectrum. As an example, we consider the representations of the Heisenberg group in solution spaces of invariant differential equations.
Keywords: invariant differential equations, spectrum, Heisenberg group
Mots-clés : solution space.
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R. S. Ismagilov. Representations of groups in solution spaces of invariant differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 489-499. http://geodesic.mathdoc.fr/item/TMF_2005_142_3_a1/

[1] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[2] B. Kostant, “Verma modules and the existence of quasi-invariant differential operators”, Non-Commutative Harmonic Analysis, Actes du Colloque d'Analyse Harmonique Non Commutative (Marseille – Luminy, 1 au 4 Juillet 1974, French), Lect. Notes Math., 466, eds. J. Carmona, J. Dixmier, M. Vergne, Springer, Berlin, 1975, 101–128 | DOI | MR

[3] V. I. Fuschich, A. G. Nikitin, Simmetriya uravnenii kvantovoi mekhaniki, Nauka, M., 1990 | MR

[4] B. Speh, J. Funct. Anal., 33 (1979), 95–118 | DOI | MR | Zbl

[5] H. P. Yakobsen, Publ. RIMS Kyoto Univ., 22 (1986), 345–364 | DOI

[6] V. F. Molchanov, Matem. sb., 81(123):3 (1970), 358–375 | MR | Zbl

[7] V. F. Molchanov, “Maximal degenerate series representations of the universal covering of the group $SU(n,n)$”, Lie Groups and Lie Algebras. Their Representations, Generalizations, and Applications, Math. Appl. Dordr., 433, eds. B. P. Komakov, I. S. Krasil'shik, G. L. Litvinov, A. B. Sossinsky, Kluwer, Dordrecht, 1998, 313–336 | MR | Zbl

[8] H. P. Yakobsen, M. Vergne, J. Funct. Anal., 24 (1977), 52–106 | DOI | MR

[9] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatgiz, M., 1959 | MR

[10] Yu. V. Egorov, “Mikrolokalnyi analiz”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 33, ed. R. V. Gamkrelidze, VINITI, M., 1988, 5–156 | MR