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Orthogonal harmonic analysis of fractal measures

Author(s): Palle E. T. Jorgensen; Steen Pedersen
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 35-42.
MSC (1991): Primary 28A75, 42B10, 42C05; Secondary 47C05, 46L55
Posted: May 5, 1998
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Abstract: We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

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Additional Information:

Palle E. T. Jorgensen
Affiliation: Department of Mathematics, University of Iowa, Iowa City, IA 52242
Email: jorgen@math.uiowa.edu

Steen Pedersen
Affiliation: Department of Mathematics, Wright State University, Dayton, OH 45435
Email: steen@math.wright.edu

DOI: 10.1090/S1079-6762-98-00044-4
PII: S 1079-6762(98)00044-4
Keywords: Spectral pair, tiling, Fourier basis, self-similar measure, fractal, affine iteration, spectral resolution, Hilbert space
Received by editor(s): October 13, 1997
Posted: May 5, 1998
Communicated by: Yitzhak Katznelson
Copyright of article: Copyright 1998, American Mathematical Society

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