Singular measures with small \(H(p,q)\)-projections
type: Item
instance of: scholarly article
title: Singular measures with small \(H(p,q)\)-projections
zbMATH Open document ID: 1021.43006
DOI: 10.1007/BF02384774
author: Evgueni Doubtsov
published in: Arkiv för Matematik
publication date: 2003-06-16T00:00:00Z
review text: Let \(S=S_n\subset \mathbf {C}^n\), \(n\geq 2\), be the complex unit sphere and \(H(p,q)\) the space of complex spherical harmonics. For a given probability measure \(\mu\in M(S)\) on \(S\) let \(\mu_{p,q}\), \(p,q\in \mathbf {Z}^2_+\), denote the projection of \(\mu\) on \(H(p,q)\). A function \(h: \mathbf {Z}^2_+\rightarrow \mathbf {R}_+\) is called \(S\)-admissible if there exists a continuous singular probability measure \(\mu\in m(S)\) such that \(\|\mu_{p,q}\|_2=O(h(p,q))\). It is proved that if \(h(p,0)=h(0,p)=p^{-1/2}\) and \(h(p,q)=0\) if \(pq\not= 0\) then \(h\) is \(S\)-admissible.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 1928884
zbMATH Keywords: Ivashëv-Musatov's theorem
MaRDI profile type: Publication
cites work: Continuous singular measures with small Fourier-Stieltjes transforms
cites work: Henkin measures, Riesz products and singular sets
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description: scientific article; zbMATH DE number 1928884