caa a22 4500 467939365 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7643-y doi (NATIONALLICENCE)springer-10.1007/s10444-004-7643-y Lai Ming-Jun Department of Mathematics, The University of Georgia, 30602, Athens, GA, USA aut Construction of multivariate compactly supported orthonormal wavelets [Elektronische Daten] [Ming-Jun Lai] We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1,. . .,ψn with n>3 such that {2kψj(2kx−ℓ,2ky−m), k,ℓ,m∈Z, j=1,. . .,n} is an orthonormal basis for L2(ℝ2). Here, n is dependent on the size of the support of φ. With parallel processes in modern computer, it is possible to use these orthonormal wavelets for applications. Furthermore, the constructive method can be extended to construct compactly supported multi-wavelets for any given compactly supported orthonormal multi-scaling vector. Finally, we mention that the constructions can be generalized to the multivariate setting. Springer, 2006 compactly supported nationallicence orthonormal nationallicence wavelets nationallicence multi-scaling vectors nationallicence multi-wavelets nationallicence multi-resolution analysis nationallicence Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 41-56 1019-7168 25:1-3<41 2006 25 10444 https://doi.org/10.1007/s10444-004-7643-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7643-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lai Ming-Jun Department of Mathematics, The University of Georgia, 30602, Athens, GA, USA aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 41-56 1019-7168 25:1-3<41 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer