Generalized Riesz products produced from orthonormal transforms

Nikolaos Atreas; Antonis Bisbas

Colloquium Mathematicae, Tome 126 (2012), p. 141-154 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $ℳ_{p} = {m_{k}}_{k = 0}^{p - 1}$ be a finite set of step functions or real valued trigonometric polynomials on = [0,1) satisfying a certain orthonormality condition. We study multiscale generalized Riesz product measures μ defined as weak-* limits of elements $μ_{N} \in V_{N} (N \in ℕ)$ , where $V_{N}$ are $p^{N}$ -dimensional subspaces of L₂() spanned by an orthonormal set which is produced from dilations and multiplications of elements of $ℳ_{p}$ and $\bar{⋃_{N \in ℕ} V_{N}} = L ₂ ()$ . The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on multiscale Riesz products.

Publié le : 2012-01-01

Zbl 1255.42009

EUDML-ID : urn:eudml:doc:283864

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     title = {Generalized Riesz products produced from orthonormal transforms},
     journal = {Colloquium Mathematicae},
     volume = {126},
     year = {2012},
     pages = {141-154},
     zbl = {1255.42009},
     language = {en},
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Nikolaos Atreas; Antonis Bisbas. Generalized Riesz products produced from orthonormal transforms. Colloquium Mathematicae, Tome 126 (2012) pp. 141-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-1/