caa a22 4500 475743784 CHVBK 20180406123507.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/s003659910010 doi (NATIONALLICENCE)springer-10.1007/s003659910010 Biorthogonal Multiwavelets on the Interval: Cubic Hermite Splines [Elektronische Daten] [W. Dahmen, B. Han, R.-Q. Jia, A. Kunoth] Abstract. : Starting with Hermite cubic splines as the primal multigenerator, first a dual multigenerator on R is constructed that consists of continuous functions, has small support, and is exact of order 2. We then derive multiresolution sequences on the interval while retaining the polynomial exactness on the primal and dual sides. This guarantees moment conditions of the corresponding wavelets. The concept of stable completions [CDP] is then used to construct the corresponding primal and dual multiwavelets on the interval as follows. An appropriate variation of what is known as a hierarchical basis in finite element methods is shown to be an initial completion. This is then, in a second step, projected into the desired complements spanned by compactly supported biorthogonal multiwavelets. The masks of all multigenerators and multiwavelets are finite so that decomposition and reconstruction algorithms are simple and efficient. Furthermore, in addition to the Jackson estimates which follow from the exactness, one can also show Bernstein inequalities for the primal and dual multiresolutions. Consequently, sequence norms for the coefficients based on such multiwavelet expansions characterize Sobolev norms ||⋅|| Hs([0,1]) for s∈ (-0.824926,2.5) . In particular, the multiwavelets form Riesz bases for L 2 ([0,1]) . Springer-Verlag New York Inc., 2000 Key words. Hermite cubic splines, Biorthogonal multigenerator, Multiwavelets, Interval, Stable completion. AMS Classification. 41A25, 42A38, 39B62 nationallicence Dahmen W. Institut für Geometrie und Praktische Mathematik RWTH Aachen, 52056, Aachen, Germany aut Han B. Program in Applied and Computational Mathematics Princeton University Princeton, NJ 08544, USA aut Jia R.-Q Department of Mathematical Sciences, University of Alberta, T6G 2G1, Edmonton, Canada aut Kunoth A. Institut für Geometrie und Praktische Mathematik RWTH Aachen, 52056, Aachen, Germany aut https://doi.org/10.1007/s003659910010 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003659910010 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dahmen W. Institut für Geometrie und Praktische Mathematik RWTH Aachen, 52056, Aachen, Germany aut NATIONALLICENCE 700 1- Han B. Program in Applied and Computational Mathematics Princeton University Princeton, NJ 08544, USA aut NATIONALLICENCE 700 1- Jia R.-Q Department of Mathematical Sciences, University of Alberta, T6G 2G1, Edmonton, Canada aut NATIONALLICENCE 700 1- Kunoth A. Institut für Geometrie und Praktische Mathematik RWTH Aachen, 52056, Aachen, Germany aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer