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Harmonic Analysis of Fractal Measures Induced by Representations of a Certain C$^*$-Algebra
Author(s):
Palle
E. T.
Jorgensen;
Steen
Pedersen
Journal:
Bull. Amer. Math. Soc.
29
(1993),
228-234.
MSC (1991):
Primary 28A75, 42B10, 46L55
MathSciNet review:
1215311
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References |
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Additional information
References:
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- O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, {\rm vol. I, revised ed.}, Springer-Verlag, New York, 1987. MR 887100
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- K. J. Falconer, The geometry of fractal sets, Cambridge Univ. Press, London and New York, 1985. MR 867284
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- B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. \textbf{16} (1974), 101--121. MR 470754
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- J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. \textbf{30} (1981), 713--747. MR 625600
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- P. E. T. Jorgensen and S. Pedersen, Spectral theory for Borel sets in $\br ^n$ of finite measure, J. Funct. Anal. \textbf{107} (1992), 72--104. MR 1165867
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- P. E. T. Jorgensen and S. Pedersen, Sur un probl\`eme spectral alg\'ebrique, C. R. Acad. Sci. Paris S\'er. I Math \textbf{312} (1991), 495--498. MR 1099679
- [JP3]
- P. E. T. Jorgensen and S. Pedersen, Spectral duality for C$^*$-algebras and fractal measures, in preparation. MR
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- R. S. Strichartz, Self-similar measures and their Fourier transforms. {\rm I, II}, Indiana Univ. Math. J. \textbf{39} (1990), 797--817; II, Trans. Amer. Math. Soc. {\bf 336} (1993), 335--361. MR 1078738
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- R. S. Strichartz, Fourier asymptotics of fractal measures, J. Funct. Anal. \textbf{89} (1990), 154--187. MR 1040961
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- R. S. Strichartz, Wavelets and self-affine tilings, Constr. Approx. \textbf{9} (1993), 327--346. MR 1215776
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00428-2
PII:
S 0273-0979(1993)00428-2
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