Geodesic
The Minlos lemma for positive-definite functions on additive subgroups of $ℝ^n$
Studia Mathematica, Tome 126 (1997) no. 1, pp. 13-25

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Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let $G_{pc}^∧$ (resp. $G_b^∧$) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology, then φ is the Fourier transform of a Radon measure μ on $G_{pc}^∧$; if φ is continuous in the Sazonov topology, μ can be extended to a Radon measure on $G_b^∧$.
DOI : 10.4064/sm-126-1-13-25

W. Banaszczyk 1

1 
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W. Banaszczyk. The Minlos lemma for positive-definite functions on additive subgroups of $ℝ^n$. Studia Mathematica, Tome 126 (1997) no. 1, pp. 13-25. doi: 10.4064/sm-126-1-13-25

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