About: Arbitrarily sparse spectra for self-affine spectral measures

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An Entity of Type : schema:ScholarlyArticle, within Data Space : covidontheweb.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Arbitrarily sparse spectra for self-affine spectral measures
Creator	Lai, Lixiang, Chun-Kit
source	ArXiv
abstract	Given an expansive matrix $R/in M_d({/mathbb Z})$ and a finite set of digit $B$ taken from $ {/mathbb Z}^d/R({/mathbb Z}^d)$. It was shown previously that if we can find an $L$ such that $(R,B,L)$ forms a Hadamard triple, then the associated fractal self-affine measure generated by $(R,B)$ admits an exponential orthonormal basis of certain frequency set $/Lambda$, and hence it is termed as a spectral measure. In this paper, we show that if #$B<\|/det (R)\|$, not only it is spectral, we can also construct arbitrarily sparse spectrum $/Lambda$ in the sense that its Beurling dimension is zero.
has issue date	2020-06-24(xsd:dateTime)
has license	arxiv
sha1sum (hex)	637081a7b01e7a1a30fe7427ab34ec407b3c2c72
resource representing a document's title	Arbitrarily sparse spectra for self-affine spectral measures
resource representing a document's body	covid:637081a7b01e7a1a30fe7427ab34ec407b3c2c72#body_text
is schema:about of	named entity 'finite set' named entity 'disjoint union' named entity 'Hadamard' named entity 'spectral measure' named entity 'affine set' »more»

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