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Orthogonality Criteria for Multi-scaling Functions

✍ Scribed by Jian-ao Lian


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
403 KB
Volume
5
Category
Article
ISSN
1063-5203

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πŸ“œ SIMILAR VOLUMES


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✍ Xingwei Zhou; Weifeng Su πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 67 KB

Suppose that m(ΞΎ ) is a trigonometric polynomial with period 1 satisfying m(0) = 1 and |m(ΞΎ In this paper, we prove a generalization: if m(ΞΎ ) has no zeros in [-1 10 , 1 10 ] and |m( 1 6 )| + m(-1 6 )| > 0, then Ο•(x) is an orthogonal function.

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The objective of this paper is to establish certain necessary and sufficient conditions for a multi-scaling function Ο† := (Ο† 1 , . . . , Ο† r ) T to have polynomial reproduction (p. r.) of order m in terms of the eigenvalues and their corresponding eigenvectors of two finite matrices.

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Daubechies (1988, Comm. Pure Appl. Math. 41, 909-996) showed that, except for the Haar function, there exist no compactly supported orthogonal symmetric scaling functions for the dilation q = 2. Nevertheless, such scaling functions do exist for dilations q > 2 (as evidenced by Chui and Lian's const

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## Ahstrati-Cracks in cross-ply fiber-reinforced specimens generally run parallel to one family of fibers or the other, but the direction of the crack can change abruptly. This qualitative behavior is predicted by the so-called critical force fracture criterion. However, the critical force criteri