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A multifractal analysis of an interesting class of measures

100%

Bisbas A.

Colloquium Mathematicum

1996

tom 69

nr 1

37-42

Generalized Riesz products produced from orthonormal transforms

63%

Atreas N., Bisbas A.

Colloquium Mathematicum

2012

tom 126

nr 2

141-154

Let $ℳ_{p} = {m_{k}}_{k=0}^{p-1}$ be a finite set of step functions or real valued trigonometric polynomials on 𝕋 = [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(𝕋) spanned by an orthonormal set which is produced from dilations and multiplications of elements of $ℳ_{p}$ and $\overline{⋃_{N∈ ℕ} V_{N}} = L₂(𝕋)$. The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on multiscale Riesz products.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Bisbas A.

1 Atreas N.

1 2012

1 1996

Wyniki wyszukiwania

A multifractal analysis of an interesting class of measures

Generalized Riesz products produced from orthonormal transforms