2,317 research outputs found
Some open questions in analysis for Dirichlet series
We present some open problems and describe briefly some possible research
directions in the emerging theory of Hardy spaces of Dirichlet series and their
intimate counterparts, Hardy spaces on the infinite-dimensional torus. Links to
number theory are emphasized throughout the paper.Comment: To appear in the proceedings volume for the conference "Completeness
Problems, Carleson Measures, and Spaces of Analytic Functions" held at the
Mittag--Leffler Institute in 201
Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.Comment: 15 pages, 18 figure
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