Wavelets of Multiplicity r
T. N. T. Goodman, S. L. Lee · Transactions of the American Mathematical Society · 1994
Abstract. A multiresolution approximation (Km)m€Z of L2(R) is of multiplicity r> 0 if there are r functions x,..., r whose translates form a Riesz basis for V $. In the general theory we derive necessary and sufficient conditions for the translates of x,..., r, y/x,..., y/r to form a Riesz basis for V \\. The resulting reconstruction and decomposition sequences lead to the construction of dual bases for V0 and its orthogonal complement W0 in Vx. The general theory is applied in the construction of spline wavelets with multiple knots. Algorithms for the construction of these wavelets for some special cases are given. Let r be a positive integer and 1.