Generalized Riesz products produced from orthonormal transforms

• Autorzy: Nikolaos Atreas , Antonis Bisbas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 2
• Strony: 141-154

Daty

wydano

2012

Twórcy

autor

Nikolaos Atreas

• Department of Mathematics, Physics and Computer Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, 54-124 Thessaloniki, Greece

autor

Antonis Bisbas

• School of Technological Applications, Department of General Sciences, Institute of West Macedonia, Kila 50-100 Kozani, Greece

Identyfikatory

DOI

10.4064/cm126-2-1