On spectral Cantor measures. (English) Zbl 1016.28009
A probability measure in \(R^d\) is called a spectral measure if it has an orthonormal basis consisting of exponentials. This paper finds conditions for a Cantor measure to be a spectral measure. In particular, a theorem of R. S. Strichartz [J. Anal. Math. 81, 209-238 (2000; Zbl 0976.42020)] is improved, by showing that one of the conditions in the theorem is redundant.
Reviewer: Richard A.Zalik (Auburn University)
MSC:
| 28A80 | Fractals |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
Citations:
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