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- Peter R Massopust, David K Ruch, Patrick J Van Fleet
- 1996

In Chui and Wang 3], support properties are derived for a scaling function generating a function space V 0 L 2 (IR). Motivated by this work, we consider support properties for scaling vectors. In 9], Goodman and Lee derive necessary and suucient conditions for the scaling vector f 1 ; : : :; r g, r 1, to form a Riesz basis for V 0 and develop a general… (More)

- David K Ruch, Patrick J Van Fleet
- 2004

This paper considers Gibbs' phenomenon for scaling vectors in L 2 (R). We first show that a wide class of multiresolution analyses suffer from Gibbs' phenomenon. To deal with this problem, in [11], Walter and Shen use an Abel summation technique to construct a positive scaling function P r , 0 < r < 1, from an orthonormal scaling function φ that generates V… (More)

Multiwavelet decompositions are based on scaling vectors satisfying matrix reenement equations. The support and linear independence of scaling vectors play an essential role in the study of multiwavelets. In this paper we relate these properties with the coeecients in the matrix reenement equation satissed by the scaling vector.

- David K Ruch, Patrick J Van Fleet
- 1996

A generalization of McFarland's iterative scheme 12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of… (More)

In this paper, we outline a method for constructing nonnegative scaling vectors on the interval. Scaling vectors for the interval have been constructed in [1–3]. The approach here is different in that the we start with an existing scaling vector Φ that generates a multi-resolution analysis for L 2 (R) to create a scaling vector for the interval. If desired,… (More)

We present a backward biorthogonalization technique for giving an orthogonal projection of a biorthogonal expansion onto a smaller subspace, reducing the dimension of the initial space by dropping d basis functions. We also determine which basis functions should be dropped to minimize the L 2 distance between a given function and its projection. This… (More)

One advantage of scaling vectors over a single scaling function is the compatibility of symmetry and orthogonality. This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vector Φ. Some general results on scaling vectors and vanishing moments are developed, as well as some necessary… (More)

- David K Ruch, Patrick J Van Fleet, Patrick J Van, Fleet
- 2003

In [14], Walter and Shen use an Abel summation technique to construct a positive scaling function P r , 0 < r < 1, from an orthonormal scaling function φ that generates V 0. A reproducing kernel can in turn be constructed using P r. This kernel is also positive, has unit integral, and approximations utilitizing it display no Gibbs' phenomenon. These results… (More)

- David K Ruch, Patrick J V An Fleet
- 1999

Let be a compactly supported, orthonormal scaling function that generates the linear space V0 2 L2IR. We are motivated by the work of Walter and Shen 77. In this paper, the authors use an Abel summation technique to build a positive scaling function Pr, 0 r 1, for the space V0. A reproducing kernel can in turn be constructed using Pr. This kernel is also… (More)

- David Ruch, Jianzhong Wang
- 1996

The purpose of this paper is to study the relationships between the support of a reenable distribution and the global and local linear independence of the integer translates of : It has been shown elsewhere that a compactly supported distribution has globally independent integer translates if and only if has minimal convex support. However, such a… (More)

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