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Spherical Harmonics on the Heisenberg Group

  • Peter C. Greiner (a1)
Extract

H1. Equip ℝ3 with the group law

(1.1)

where (z, t) stands for (x, y, t). This is a nilpotent Lie group, usually referred to as the first Heisenberg group, H 1. In general H k denotes ℝ2k+1 equipped with a similar group law, namely

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References
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1. Erdélyi, A., et al, Higher Transcendental functions, v. 1 and v. 2, Bateman Manuscript Project, McGraw-Hill, New York, 1955.
2. Folland, G. B., A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), pp. 373-376.
3. Folland, G. B. and Stein, E. M., Estimates for the db-complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), pp. 429-522.
4. Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents, Acta Math. 139 (1977), pp. 95-153.
5. Greiner, P. C., Kohn, J. J. and Stein, E. M., Necessary and sufficient conditions for the solvability of the Lewy equation, Proc. Nat. Acad, of Sciences, U.S.A., 72 (1975), pp. 3287-3289.
6. Greiner, P. C. and Stein, E. M., Estimates for the d-Neumann problem, Mathematical Notes Series, no. 19, Princeton Univ. Press, Princeton, N.J., 1977.
7., On the solvability of some differential operators of type Db, Proc. of the Seminar on Several Complex Variables, Cortona, Italy, 1976-1977, pp. 106-165.
8. Kuranishi, M., A priori estimate in strongly pseudo-convex CR structure over small balls, Preprint.
9. Miiller, C., Spherical harmonics, Lecture Notes in Math., v. 17, Springer-Verlag, Berlin, 1966.
10. Szegô, G-, Orthogonal polynomials, Amer. Math. Soc. Colloquium Publications, v. 23, Amer. Math. Soc, Providence, R.I., 1939.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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