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Geometric Fourier analysis

Antonio Cordoba (1982)

Annales de l'institut Fourier

In this paper we continue the study of the Fourier transform on R n , n 2 , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of log ( N ) , where N is the number of equal angles considered in R 2 . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of R n , n 2 , of fixed eccentricity...

Hausdorff and Fourier dimension

Thomas William Körner (2011)

Studia Mathematica

There is no constraint on the relation between the Fourier and Hausdorff dimension of a set beyond the condition that the Fourier dimension must not exceed the Hausdorff dimension.

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

Kyurkchiev, Nikolay, Andreev, Andrey (2013)

Serdica Journal of Computing

ACM Computing Classification System (1998): G.1.2.Moduli for numerical finding of the polynomial of the best Hausdorff approximation of the functions which differs from zero at just one point or having one jump and partially constant in programming environment MATHEMATICA are proposed. They are tested for practically important functions and the results are graphically illustrated. These moduli can be used for scientific research as well in teaching process of Approximation theory and its application....

Henkin measures, Riesz products and singular sets

Evgueni Doubtsov (1998)

Annales de l'institut Fourier

The mutual singularity problem for measures with restrictions on the spectrum is studied. The d -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.

Hurewicz scheme

Michal Staš (2008)

Acta Universitatis Carolinae. Mathematica et Physica

Ideal norms and trigonometric orthonormal systems

Jörg Wenzel (1994)

Studia Mathematica

We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.

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