caa a22 4500 463246985 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s00041-006-6021-1 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6021-1 Ehler Martin Department of Mathematics and Computer Science, Hans-Meerwein-Strasse, 35032 Marburg, Germany aut On Multivariate Compactly Supported Bi-Frames [Elektronische Daten] [Martin Ehler] In this article, we construct compactly supported multivariate pairs of dual wavelet frames, shortly called bi-frames, for an arbitrary dilation matrix. Our construction is based on the mixed oblique extension principle, and it provides bi-frames with few wavelets. In the examples, we obtain optimal bi-frames, i.e., primal and dual wavelets are constructed from a single fundamental refinable function, whose mask size is minimal w.r.t. sum rule order and smoothness. Moreover, the wavelets reach the maximal approximation orderw.r.t. the underlying refinable function. For special dilation matrices, we derive very simple but optimal arbitrarily smooth bi-frames in arbitrary dimensions with only two primal and dual wavelets. Birkhauser Boston, 2007 Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 511-532 1069-5869 13:5<511 2007 13 41 https://doi.org/10.1007/s00041-006-6021-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6021-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ehler Martin Department of Mathematics and Computer Science, Hans-Meerwein-Strasse, 35032 Marburg, Germany aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 511-532 1069-5869 13:5<511 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer