Dense analytic subspaces in fractal $L^{2}$-spaces
| dc.creator | Jorgensen, Palle E. T. | |
| dc.creator | Pedersen, Steen | |
| dc.date | 1997-09-30 | |
| dc.date.accessioned | 2026-07-07T09:13:51Z | |
| dc.date.available | 2026-07-07T09:13:51Z | |
| dc.description | We consider self-similar measures $μ$ with support in the interval $0\leq x\leq 1$ which have the analytic functions $\left\{e^{i2πnx}:n=0,1,2,... \right\} $ span a dense subspace in $L^{2}(μ) $. Depending on the fractal dimension of $μ$, we identify subsets $P\subset \mathbb{N}_{0}=\{0,1,2,... \} $ such that the functions $\{e_{n}:n\in P\} $ form an orthonormal basis for $L^{2}(μ) $. We also give a higher-dimensional affine construction leading to self-similar measures $μ$ with support in $\mathbb{R}^ν$. It is obtained from a given expansive $ν$-by-$ν$ matrix and a finite set of translation vectors, and we show that the corresponding $L^{2}(μ) $ has an orthonormal basis of exponentials $e^{i2πλ\cdot x}$, indexed by vectors $λ$ in $\mathbb{R}^ν$, provided certain geometric conditions (involving the Ruelle transfer operator) hold for the affine system. | |
| dc.description | 41 pages, 5 figures, AMS-LaTeX v1.2b with EPS and LaTeX "picture" graphics. Authors Palle E.T. Jorgensen (The University of Iowa) and Steen Pedersen (Wright State University) | |
| dc.identifier | https://arxiv.org/abs/funct-an/9709007 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9709007 | |
| dc.identifier | J. Analyse Math. 75 (1998), 185--228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152469 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42C05, 22D25, 46L55, 47C05 | |
| dc.title | Dense analytic subspaces in fractal $L^{2}$-spaces | |
| dc.type | text |