Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T03:51:45.153Z Has data issue: false hasContentIssue false
  • English
  • Français

Spherical Harmonics on the Heisenberg Group

Published online by Cambridge University Press:  20 November 2018

Peter C. Greiner
Peter C. Greiner*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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, H1. In general Hk denotes ℝ2k+1 equipped with a similar group law, namely

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 383 - 396
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Erdélyi, A., et al, Higher Transcendental functions, v. 1 and v. 2, Bateman Manuscript Project, McGraw-Hill, New York, 1955.Google Scholar
2. Folland, G. B., A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), pp. 373-376.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
8. Kuranishi, M., A priori estimate in strongly pseudo-convex CR structure over small balls, Preprint.Google Scholar
9. Miiller, C., Spherical harmonics, Lecture Notes in Math., v. 17, Springer-Verlag, Berlin, 1966.Google Scholar
10. Szegô, G-, Orthogonal polynomials, Amer. Math. Soc. Colloquium Publications, v. 23, Amer. Math. Soc, Providence, R.I., 1939.Google Scholar