-spaces of conjugate systems on local fields
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.
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....
The mutual singularity problem for measures with restrictions on the spectrum is studied. The -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.
AMS Subject Classification 2010: 11M26, 33C45, 42A38.Necessary and sufficient conditions for absence of zeros of ζ(s) in the half-plane σ ... Expansion of holomorphic functions in series of Hermite polynomials ...