Gazeau, Jean Pierre; Spiridonov, Vyacheslav Toward discrete wavelets with irrational scaling factor. (English) Zbl 0861.42024 J. Math. Phys. 37, No. 6, 3001-3013 (1996). 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. Cited in 4 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 82D25 Statistical mechanics of crystals Keywords:multiresolution analysis; discrete wavelets; irrational scaling factor; Haar-type wavelets; dilation factors; summation formulas PDFBibTeX XMLCite \textit{J. P. Gazeau} and \textit{V. Spiridonov}, J. Math. Phys. 37, No. 6, 3001--3013 (1996; Zbl 0861.42024) Full Text: DOI References: [1] DOI: 10.1088/0034-4885/54/11/001 · doi:10.1088/0034-4885/54/11/001 [2] DOI: 10.1103/PhysRevA.52.1909 · doi:10.1103/PhysRevA.52.1909 [3] DOI: 10.1080/10586458.1992.10504561 · Zbl 0788.65129 · doi:10.1080/10586458.1992.10504561 [4] DOI: 10.1007/BF02020331 · Zbl 0079.08901 · doi:10.1007/BF02020331 [5] Bertrand A., C. R. Acad. Sci. Paris 285 pp 419– (1977) [6] DOI: 10.1109/18.119723 · Zbl 0742.42012 · doi:10.1109/18.119723 [7] Cavaretta A. S., Mem. Am. Math. Soc. 93 pp 1– (1991) · doi:10.1090/memo/0453 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.