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We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

Copyright 1998 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 35-42
• Publisher Identifier: S 1079-6762(98)00044-4
• 1991 Mathematics Subject Classification. Primary 28A75, 42B10, 42C05; Secondary 47C05, 46L55
• Key words and phrases. Spectral pair, tiling, Fourier basis, self-similar measure, fractal, affine iteration, spectral resolution, Hilbert space
• Received by the editors October 13, 1997
• Posted on May 5, 1998
• Communicated by Yitzhak Katznelson
• Comments (When Available)

Palle E. T. Jorgensen

Department of Mathematics, University of Iowa, Iowa City, IA 52242

E-mail address: jorgen@math.uiowa.edu

Steen Pedersen

Department of Mathematics, Wright State University, Dayton, OH 45435

E-mail address: steen@math.wright.edu