Journal article
Harmonic analysis and fractal limit-measures induced by representations of a certain C-algebra
Journal of functional analysis, Vol.125(1), pp.90-110
1994
DOI: 10.1006/jfan.1994.1118
Abstract
We describe a class of measurable subsets Ω in R d such that L 2 ( Ω ) has an orthogonal basis of frequencies e λ ( x ) = e i 2πλ · x ( x ∈ Ω ) indexed by λ ∈ Λ ⊂ R d . We show that such spectral pairs ( Ω , Λ ) have a self-similarity which may be used to generate associated fractal measures μ (typically with Cantor set support). The Hilbert space L 2 (μ) does not have a total set of orthogonal frequencies; but a harmonic analysis of μ may be built instead from a natural representation of the Cuntz C *-algebra which is constructed from a pair of lattices supporting the given spectral pair ( Ω , Λ ). We show conversely that such a pair may be reconstructed from a certain Cuntz-representation given to act on L 2 (μ).
Details
- Title: Subtitle
- Harmonic analysis and fractal limit-measures induced by representations of a certain C-algebra
- Creators
- Palle E.T JorgensenSteen Pedersen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.125(1), pp.90-110
- DOI
- 10.1006/jfan.1994.1118
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1994
- Academic Unit
- Mathematics
- Record Identifier
- 9983986099402771
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