David Karl Ruch

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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)
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)
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)
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)
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)
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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