The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
A Poisson Formula for Semi-Simple Lie Groups
Abstract
for some bounded function h on the boundary of the disc. The function h(z) determines a function h(g) on G by setting h(g) = h(g(O)). If h(z) is harmonic, it may be shown that h(g) is annihilated by a certain class of differential operators on G. The Poisson formula (1) may be used to express h(g), and we find that here it takes on a particularly simple form. Namely, if we denote by m the normalized Lebesgue measure on {j z I = 1}, and by gm, the transform of this measure by the group element g E G, then it can be seen that (1) becomes
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Doob, J. L., & Doob, J. L. (1953) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,053
Loève, M. (1963) · Andalas University Repository (Andalas University) · Cited by 5,938
Chevalley, C. C. (1946) · CERN Document Server (European Organization for Nuclear Research) · Cited by 945
L'integration dans les groupes topologiques et ses applications
WEIL, A. A. (1951) · Hermann eBooks · Cited by 778
A new proof of E. Cartan’s theorem on the topology of semi-simple groups
Mostow, G. D. (1949) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1949-09325-4 · Cited by 47
Cited by
Furstenberg, H. (1963) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1963-0163345-0 · Cited by 984
Self-citationLectures on Spaces of Nonpositive Curvature
Ballmann, W. (1995) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9240-7 · Cited by 513
On fundamental groups of complete affinely flat manifolds
Milnor, J. (1977) · Advances in Mathematics · doi:10.1016/0001-8708(77)90004-4 · Cited by 266
Metadata
- Authors
- Furstenberg, H.
- Venue
- The Annals of Mathematics
- Publisher
- JSTOR
- Published
- 1963-03
- Volume
- 77
- Issue
- 2
- Pages
- 335
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2065516294
- Cited by
- 428
- References
- 5
- FWCI
- 4.96
- Type
- journal article
- Language
- en
- Open access
- closed
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