N–Term Approximation in Anisotropic Function Spaces

✍ Scribed by Reinhard Hochmuth

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 272 KB
• Volume: 244
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/1522-2616(200210)244:1<131::aid-mana131>3.0.co;2-g

✦ Synopsis

In L 2 ((0, 1) 2 ) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.