Orthogonal harmonic analysis

of fractal measures

Authors:
Palle E. T. Jorgensen and Steen Pedersen

Journal:
Electron. Res. Announc. Amer. Math. Soc. **4** (1998), 35-42

MSC (1991):
Primary 28A75, 42B10, 42C05; Secondary 47C05, 46L55

DOI:
https://doi.org/10.1090/S1079-6762-98-00044-4

Published electronically:
May 5, 1998

MathSciNet review:
1618687

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S1079-6762-98-00044-4

Keywords:
Spectral pair,
tiling,
Fourier basis,
self-similar measure,
fractal,
affine iteration,
spectral resolution,
Hilbert space

Received by editor(s):
October 13, 1997

Published electronically:
May 5, 1998

Communicated by:
Yitzhak Katznelson

Article copyright:
© Copyright 1998
American Mathematical Society