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On various types of convergence of positive definite functions on foundation semigroups

Published online by Cambridge University Press:  24 October 2008

M. Lashkarizadeh-Bami
M. Lashkarizadeh-Bami
Affiliation:
Department of Pure Mathematics, University of Sheffield
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Extract

As is known, on a locally compact group G, the mere assumption of pointwise convergence of a sequence (n) of continuous positive definite functions implies uniform convergence of (n) to on compact subsets of G. This result was first proved in 1947 by Raikov8 (and independently by Yoshizawa9). An interesting discussion of the relationship between such theorems and various Cramr-Lvy theorems of the 1920s and 1930s, concerning the Central Limit Problem of probability, is given by McKennon(7, p. 62).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 325 - 330
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

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