.... Keywords: operator equations; multiscale methods; adaptive algorithms; sparse matrices; Banach frames; norm equivalences. 1. Introduction In recent years, wavelets have been very successfully applied to several tasks. In signal/image analysis/ compression, wavelet schemes are by now already well...

... mapping · · 0 Ω p face order preserving internal point norm equivalence Sobolev space Hbs Ω Hbs Ω P matching Berrone S Emmel L POLITOLib transfinite interpolation embedding fictitious domain methods wavelets on the interval Wavelet Element Method tensor product refinement matrices norm...

... as biorthogonal wavelets. The Fast Wavelet Transform (FWT) is provided. The chapter describes the core property of wavelets for the numerical treatment of elliptic partial differential equations, the so-called norm equivalences. It is shown that such equivalences are guaranteed by two estimates known from...