✦ LIBER ✦

Compactly Supported Orthogonal Symmetric Scaling Functions

✍ Scribed by Eugene Belogay; Yang Wang

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 148 KB
Volume: 7
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1999.0265

No coin nor oath required. For personal study only.

✦ Synopsis

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 construction (1995, Appl. Comput. Harmon. Anal. 2, 68-84) for q = 3); these functions are the main object of this paper. We construct new symmetric scaling functions and introduce the "Batman" family of continuous symmetric scaling functions with very small supports. We establish the exact smoothness of the "Batman" scaling functions using the joint spectral radius technique.

📜 SIMILAR VOLUMES

Orthogonality Criteria for Compactly Sup

Orthogonality Criteria for Compactly Supported Scaling Functions

✍ Karlheinz Gröchenig 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 196 KB

Compactly Supported Correlation Function

Compactly Supported Correlation Functions

✍ Tilmann Gneiting 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 155 KB

This article proposes compactly supported correlation functions, which parameterize the smoothness of the associated stationary and isotropic random field. The constructions are straightforward, and compact support is relevant for various ends: computationally efficient spatial prediction, fast and

A Construction of Orthogonal Compactly S

A Construction of Orthogonal Compactly Supported Multiwavelets on R2

✍ Bruce Kessler 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 351 KB

This paper will provide the general construction of the continuous, orthogonal, compactly supported multiwavelets associated with a class of continuous, orthogonal, compactly supported scaling functions that contain piecewise linears on a uniform triangulation of R 2 . This class of scaling function

Multiresolution Analysis by Infinitely D

Multiresolution Analysis by Infinitely Differentiable Compactly Supported Functions

✍ N. Dyn; A. Ron 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 398 KB

Compactly Supported Tight Frames Associa

Compactly Supported Tight Frames Associated with Refinable Functions

✍ Charles K. Chui; Wenjie He 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 221 KB

It is well known that in applied and computational mathematics, cardinal B-splines play an important role in geometric modeling (in computeraided geometric design), statistical data representation (or modeling), solution of differential equations (in numerical analysis), and so forth. More recently,

Dual reciprocity method using compactly

Dual reciprocity method using compactly supported radial basis functions

✍ Chen, C. S. ;Brebbia, C. A. ;Power, H. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 208 KB 👁 2 views

Compactly supported radial basis functions have been used to interpolate the forcing term in the DRM. The resulting DRM matrix is sparse and our approach is very accurate and ecient. Our proposed method is especially attractive for large scale problems.