Nonseparable, Compactly Supported Interpolating Refinable Functions with Arbitrary Smoothness

✍ Scribed by Josip Derado

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 731 KB
• Volume: 10
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1006/acha.2000.0334

✦ Synopsis

In this paper we construct families of compactly supported nonseparable interpolating refinable functions with arbitrary smoothness (or regularity). The symbols for the newly constructed scaling functions are given by a simple formula related to the Bernstein polynomials. The emphasis of the paper is to show that under an easy-to-verify geometric condition these families satisfy Cohen's condition, and they have arbitrarily high regularity. Furthermore, the constructed scaling functions satisfy, under the same geometrical condition, the Strang-Fix conditions of arbitrarily high order, which implies that corresponding interpolating schemes have arbitrarily high accuracy.