caa a22 4500 467939136 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7623-2 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7623-2 Tight frames and geometric properties of wavelet sets [Elektronische Daten] [John Benedetto, Songkiat Sumetkijakan] A construction for providing single dyadic orthonormal wavelets in Euclidean space ℝd is given. It is called the general neighborhood mapping construction. The fact that one wavelet is sufficient to generate an orthonormal basis for L2(ℝd) is the critical issue. The validity of the construction is proved, and the construction is implemented computationally to provide a host of examples illustrating various geometrical properties of such wavelets in the spectral domain. Because of the inherent complexity of these single orthonormal wavelets, the method is applied to the construction of single dyadic tight frame wavelets, and these tight frame wavelets can be surprisingly simple in nature. The structure of the spectral domains of the wavelets arising from the general neighborhood mapping construction raises a basic geometrical question. There is also the question of whether or not the general neighborhood mapping construction gives rise to all single dyadic orthonormal wavelets. Results are proved giving partial answers to both of these questions. Springer, 2006 frames nationallicence wavelets nationallicence Benedetto John Department of Mathematics, University of Maryland, College Park, 20742, MD, U.S.A. aut Sumetkijakan Songkiat Department of Mathematics, Chulalongkorn University, 10330, Bangkok, Thailand aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 35-56 1019-7168 24:1-4<35 2006 24 10444 https://doi.org/10.1007/s10444-004-7623-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7623-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Benedetto John Department of Mathematics, University of Maryland, College Park, 20742, MD, U.S.A aut NATIONALLICENCE 700 1- Sumetkijakan Songkiat Department of Mathematics, Chulalongkorn University, 10330, Bangkok, Thailand aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 35-56 1019-7168 24:1-4<35 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer