A new class of multi-wavelet bases: V-system (Q1943020)

A \(V\)-system is a complete orthogonal system of functions supported on \([0,1]\) that is generated by a finite number of Legendre polynomials together with the dilations and translations of a function generator that consists of a finite number of continuous and discontinuous functions. The authors show that a \(V\)-system is a special multi-wavelet system whose scaling vector is given by the Legendre polynomials and whose multi-wavelet is given by the corresponding function generator. A number of examples closes the paper.