Interval-adapted wavelet basis
= Interval-adapted wavelet basis
An interval-adapted wavelet basis is an <orthonormal basis> of $L^2[0,1]$ made of a finite coarse <scaling function> family and resolution-indexed <wavelets>. A localized construction modifies only a bounded number of functions near each endpoint at every level. Boundary modification must preserve nested refinement spaces and the required <vanishing moments>; simple restriction of a whole-line basis does not do so.