Asymptotic distribution of functions on compact homogeneous spaces. (English) Zbl 0668.10054

Blümlinger, M.; Drmota, M.; Tichy, R. F.

Ann. Mat. Pura Appl., IV. Ser. 152, 79-93 (1988).

The authors study distribution properties of continuous functions on compact connected homogeneous Riemannian manifolds \(X\) (generalizing known results in the special case \(X=\mathbb{R}^n/\mathbb{Z}^n)\). It is proved that almost all functions are uniformly distributed and almost no functions are well distributed. Similar results are obtained for sequences.
The authors also announce a law of iterated logarithm for the discrepancy of functions on compact connected Riemannian manifolds [using results of W. Philipp, Mem. Am. Math. Soc. 114 (1971; Zbl 0224.10052)].

Reviewer: Harald Rindler (Wien)

MSC:

11K06	General theory of distribution modulo \(1\)
43A85	Harmonic analysis on homogeneous spaces
60F05	Central limit and other weak theorems

Keywords:

uniform distribution; well distribution; continuous functions; compact connected homogeneous Riemannian manifolds; law of iterated logarithm; discrepancy of functions; compact connected Riemannian manifolds

Citations:

Zbl 0224.10052

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