On the Support Properties of Scaling Vectors

  title={On the Support Properties of Scaling Vectors},
  author={Peter R. Massopust and David Karl Ruch and Patrick J. Van Fleet},
  journal={Applied and Computational Harmonic Analysis},
Abstract C. K. Chui and J. Z. Wang [ J. Approx. Theory 71 (1992), 263–304] derived support properties for a scaling function generating a function space V 0 ⊆ L 2 (open face R). Motivated by this work, we consider support properties for scaling vectors. T. N. T. Goodman and S. L. Lee [ Trans. Amer. Math. Soc. 342, No. 1 (Mar. 1994), 307–324] derived necessary and sufficient conditions for the scaling vector {φ 1 , … , φ r }, r ≥1, to form a Riesz basis for V 0 and develop a general theory for… 

Positive Scaling Vectors on the Interval

In (14), Walter and Shen use an Abel summation technique to construct a positive scaling function Pr, 0 < r < 1, from an orthonormal scaling functionthat gener- ates V0. A reproducing kernel can in

Stability and linear independence associated with scaling vectors

Stable scaling vectors often serve as generators of multiresolution analyses (MRAs) and therefore play an important role in the study of multiwavelets and most useful MRA generators are also linearly independent.

Study of Linear Independence and Accuracy of Scaling Vectors via Two-scale Factors

A scaling vector φ = (φ1, · · · , φr) is a compactly supported vector-valued distribution that satisfies a matrix refinement equation φ(x) = P Pkφ(2x−k), where (Pk) is a finite matrix sequence. We

Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scaleN

AbstractIn this paper we show how wavelets originating from multiresolution analysis of scaleN give rise to certain representations of the Cuntz algebrasON, and conversely how the wavelets can be

Cuntz algebras and multiresolution wavelet analysis of scale N

In this paper we show how wavelets originating from multireso-lution analysis of scale N give rise to certain representations of the Cuntz algebras O N , and conversely how the wavelets can be

Orthogonality Criteria for Multi-scaling Functions

Necessary and sufficient conditions for the orthonormality of a multi-scaling function φ with integer dilation factoraand multiplicityrare established. Here φ := (φ1, … , φr)Tand satisfies φ(x)

Multiwavelets--theory and applications

A function (t) is reenable if it satisses a dilation equation (t) = P k C k (2t ? k). A reenable function (scaling function) generates a multiresolution analysis (MRA): Set of T 1 j=?1 V j = f0g, and

Vanishing moments for scaling vectors

  • D. Ruch
  • Mathematics
    Int. J. Math. Math. Sci.
  • 2004
This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vector Φ, an orthogonal, symmetric scaling vector with one vanishing moment having minimal support.



A general framework of compactly supported splines and wavelets

Using The Refinement Equation For The Construction of Pre-Wavelets VI: Shift Invariant Subspaces

This paper follows the format of our tutorial on multivariate wavelet decomposition, [6]. We demonstrate here that the methods employed by Jia and Micchelli [2] can be extended to subspaces of L 2(ℝ

A Practical Guide to Splines

  • C. D. Boor
  • Mathematics
    Applied Mathematical Sciences
  • 1978
This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.

An introduction to wavelets

An Overview: From Fourier Analysis to Wavelet Analysis, Multiresolution Analysis, Splines, and Wavelets.

Orthonormal bases of compactly supported wavelets

This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.

Ten Lectures on Wavelets

This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.

Fractal Functions and Wavelet Expansions Based on Several Scaling Functions

We present a method for constructing translation and dilation invariant functions spaces using fractal functions defined by a certain class of iterated function systems. These spaces generalize the