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Wavelet sets accumulating at the origin. (English) Zbl 1268.42064

Real Anal. Exch. 35(2009-2010), No. 2, 463-478 (2010); errata ibid. 36(2010-2011), No. 1, 243-244 (2011).
Summary: For a natural number \(n\), selecting a \(2n\)-interval symmetric wavelet set by making use of a result of N. Arcozzi, B. Behera, and S. Madan [J. Geom. Anal. 13, 557–579 (2003; Zbl 1051.42022)], we construct a family of symmetric wavelet sets accumulating at the origin. Such a family of wavelet sets is also obtained from a family of symmetric six-interval wavelet sets provided by them in the same paper. Three-interval wavelet sets are employed in having a family of wavelet sets accumulating at the origin which are non-symmetric. Further, we obtain a larger class of \(H^{2}\)-wavelet sets accumulating at the origin, which include the one given by B. Behera [Bull. Polish Acad. Sci. Math. 52, 169–178 (2004; Zbl 1096.42023)]. Finally, non-MSF non-MRA wavelets are obtained through the selected family of \(2n\)-interval symmetric wavelet sets.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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