Displaying similar documents to “The order structure of the space of measures with continuous translation”

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let L , M be Archimedean Riesz spaces and b ( L , M ) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of b ( L , M ) to be an ordered vector subspace of b ( L , M ) such that the elements of preserve disjointness and any pair of operators in has a supremum in b ( L , M ) that belongs to . It turns out that the lattice operations in any Lamperti Riesz subspace of b ( L , M ) are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem...

An F. and M. Riesz theorem for bounded symmetric domains

R. G. M. Brummelhuis (1987)

Annales de l'institut Fourier

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We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains. The proof uses a criterion for absolute continuity involving L p spaces with p < 1 : A measure μ on a compact metrisable group K is absolutely continuous with respect to Haar measure d k on K if for some p < 1 a certain subspace of L p ( K , d k ) which is related to μ has sufficiently...

A microlocal F. and M. Riesz theorem with applications.

Raymondus G. M. Brummelhuis (1989)

Revista Matemática Iberoamericana

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Consider, by way of example, the following F. and M. Riesz theorem for R: Let μ be a finite measure on R whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ)...

On summability of measures with thin spectra

Maria Roginskaya, Michaël Wojciechowski (2004)

Annales de l’institut Fourier

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We study different conditions on the set of roots of the Fourier transform of a measure on the Euclidean space, which yield that the measure is absolutely continuous with respect to the Lebesgue measure. We construct a monotone sequence in the real line with this property. We construct a closed subset of d which contains a lot of lines of some fixed direction, with the property that every measure with spectrum contained in this set is absolutely continuous. We also give examples of sets...

Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, Dachun Yang (2004)

Studia Mathematica

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Suppose that μ is a Radon measure on d , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces p q s ( μ ) for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function...