Wavelet Sets Accumulating at the Origin

Abstract

For a natural number $n$, selecting a $2n$-interval symmetric wavelet set by making use of a result of Arcozzi, Behera and Madan [J. Geom. Anal. 13 (2003), 557-579], 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 Behera in [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178]. Finally, non-MSF non-MRA wavelets are obtained through the selected family of $2n$-interval symmetric wavelet sets.