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Some remarks on Fourier seminorms. (English) Zbl 0635.60035

In several papers and in a monograph the reviewer has used a semi-norm, called Gaussian semi-norm, on the algebra of signed measures on the line R and the Euclidean space \(R^{(k)}\), \(k>1\). F. Zítek [ibid. 95, 62-65 (1970; Zbl 0224.46042)] showed that this semi-norm on R and for signed measures, positive on the complement of the zero point, was equivalent with a certain Fourier semi-norm introduced by him. In the paper under review it is shown that there is also such an equivalence on \(R^{(k)}\).
Reviewer: H.Bergström

MSC:

60F99 Limit theorems in probability theory
28A99 Classical measure theory

Citations:

Zbl 0224.46042