Titlebook: Analysis and Probability; Wavelets, Signals, F Palle E.T. Jorgensen Textbook 2006 Springer-Verlag New York 2006 Excel.Measure.Signal.Symbol

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https://doi.org/10.1007/978-3-642-78105-6 frequencies may then be realized by a certain dual rank-. lattice. In this case, the inverse relation is formulated as a duality principle for lattices; see, for example, [JoPe93] for a survey of this point.

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Introduction: Measures on path space,es .. This scale-similarity is a special case of a more general notion of .. We will later see that the more general idea of self-similarity is needed for our understanding of fractals and symbolic dynamics.

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A case study: Duality for Cantor sets,ists and will be indexed by an arithmetic progression of (Fourier) frequencies, i.e., by integers times the inverse wave length. Similarly, in higher dimensions ., we define periodicity in terms of a lattice of rank .. The principle states that for .-periodic functions on ?., the appropriate Fourier

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The minimal eigenfunction,d 8. We wish to examine a variation of scale, i.e., examine the effect on the Perron-Frobenius-Ruelle theory induced by a change of scale in a wavelet basis. After stating a general result (Theorem 6.1.1), we take a closer look at a single example: Recall that Haar’s wavelet is dyadic, i.e., it is a

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