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Toward discrete wavelets with irrational scaling factor. (English) Zbl 0861.42024

Summary: Scaling equations determining Haar-type wavelets are considered for three Pisot numbers \(\beta= (1+\sqrt{5})/2\), \(1+\sqrt{2}\), \(2+\sqrt{3}\) appearing as dilation factors in scale invariance of observed diffraction patterns of quasicrystals. Simple summation formulas for exponentials of the corresponding \(\beta\) integers are derived.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
82D25 Statistical mechanics of crystals
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