FOURIER SERIES ON FRACTALS: A PARALLEL WITH WAVELET THEORY
FOURIER SERIES ON FRACTALS: A PARALLEL WITH WAVELET THEORY
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DOI：
10.1090/conm/464/09077
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发表时间：
2007-09
期刊：
影响因子：
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通讯作者：
D. Dutkay;P. Jorgensen
中科院分区：
文献类型：
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作者：
D. Dutkay;P. Jorgensen
研究了Hilbert空间L2（μ）中复指数和Fourier频率的正交关系，测度μ来自迭代函数系（IFS）.这包括复杂动力学中的平衡测量。出于应用的动机，我们绘制平行的分形测度的分析，一方面，和小波的几何形状的其他。我们的动机是谱理论的commuting偏微分算子和相关的对偶概念。虽然最初规定的有界和开放区域的R d，他们已经发现重新在理论的分形和小波。我们包括一个历史草图与早期运营商理论的问题。
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces L 2 (µ) with measures µ arising from iterated function systems (IFS). This includes equilibrium mea- sures in complex dynamics. Motivated by applications, we draw parallels between analysis of fractal measures on the one hand, and the geometry of wavelets on the other. We are motivated by spectral theory for com- muting partial differential operators and related duality notions. While stated initially for bounded and open regions in R d , they have since found reformulations in the theory of fractals and wavelets. We include a historical sketch with questions from early operator theory.