Wavelets on intervals derived from arbitrary compactly supported biorthogonal multiwavelets

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems are defined bounded intervals or domains. Therefore, it is important both theory application to construct all possible wavelets some desired properties from (bi)orthogonal line. Vanishing moments compactly supported key property for sparse wavelet representations closely linked polynomial reproduction their underlying refinable (vector) functions. Boundary low order vanishing often lead undesired boundary artifacts as well reduced sparsity approximation orders near boundaries applications. From any arbitrarily given multiwavelet line, this paper we propose two different approaches construct/derive locally $[0,\infty)$ $[0,1]$ without prescribed moments, reproduction, and/or homogeneous conditions. The first approach generalizes classical scalar multiwavelets, while second direct explicitly involving dual functions multiwavelets. (Multi)wavelets satisfying conditions will also be addressed. Though constructing orthogonal much easier than biorthogonal counterparts, show that cannot if these satisfy Dirichlet condition. Several examples multiwavelets interval provided illustrate our construction proposed algorithms.