A generalization of Wienner's criteria for the continuity of a Borel measure

Jean-Marc Belley; Pedro Morales

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Remarks on compactly generated Abelian topological groups

K. Urbanik (1960)

Colloquium Mathematicum

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The Minlos lemma for positive-definite functions on additive subgroups of $ℝ^{n}$

W. Banaszczyk (1997)

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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 $G_{p c}^{\land}$ (resp. $G_{b}^{\land}$ ) 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...