Displaying similar documents to “ K -distance sets, Falconer conjecture, and discrete analogs.”

Some remarks on restriction of the Fourier tranform for general measures.

Per Sjölin, Fernando Soria (1999)

Publicacions Matemàtiques

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In this paper we establish a formal connection between the average decay of the Fourier transform of functions with respect to a given measure and the of that measure. We also present a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension n - 1 + α, with 0 < α < 1.

On set covariance and three-point test sets

Jan Rataj (2004)

Czechoslovak Mathematical Journal

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The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of ℝ d is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives...

Contracting-on-Average Baker Maps

Michał Rams (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

Spaces of σ-finite linear measure

Ihor Stasyuk, Edward D. Tymchatyn (2013)

Colloquium Mathematicae

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Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear...