Generalized Riesz products produced from orthonormal transforms

Nikolaos Atreas, and Antonis Bisbas. "Generalized Riesz products produced from orthonormal transforms." Colloquium Mathematicae 126.2 (2012): 141-154. <http://eudml.org/doc/283864>.

@article{NikolaosAtreas2012,
abstract = {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 $μ_\{N\} ∈ V_\{N\} (N ∈ ℕ)$, 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 $\overline\{⋃_\{N∈ ℕ\} V_\{N\}\} = L₂()$. The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on multiscale Riesz products.},
author = {Nikolaos Atreas, Antonis Bisbas},
journal = {Colloquium Mathematicae},
keywords = {Riesz products; generalized Riesz products; multiscale transforms},
language = {eng},
number = {2},
pages = {141-154},
title = {Generalized Riesz products produced from orthonormal transforms},
url = {http://eudml.org/doc/283864},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Nikolaos Atreas
AU - Antonis Bisbas
TI - Generalized Riesz products produced from orthonormal transforms
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 2
SP - 141
EP - 154
AB - 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 $μ_{N} ∈ V_{N} (N ∈ ℕ)$, 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 $\overline{⋃_{N∈ ℕ} V_{N}} = L₂()$. The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on multiscale Riesz products.
LA - eng
KW - Riesz products; generalized Riesz products; multiscale transforms
UR - http://eudml.org/doc/283864
ER -