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

• Autorzy: W. Banaszczyk
• Języki publikacji: EN

Abstrakty

EN

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 $G_b^∧$.

Kategorie tematyczne

• 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
• 60B11: Probability theory on linear topological spaces
• 52A40: Inequalities and extremum problems
• 43A35: Positive definite functions on groups, semigroups, etc.
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 126
• Numer: 1
• Strony: 13-25

Daty

wydano

1997

otrzymano

1995-10-09

poprawiono

1997-06-09

Twórcy

autor

W. Banaszczyk

• Faculty of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

Bibliografia

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• [4] W. Banaszczyk, Inequalities for convex bodies and polar reciprocal lattices in $ℝ^n$ II. Application of K-convexity, Discrete Comput. Geom. 16 (1996), 305-311.
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