Point values and normalization of two-direction multiwavelets and their derivatives

Two-direction multiscaling functions φ and two-direction multiwaveletsψ associated with φ are more general and more flexible setting than one-direction multiscaling functions and multiwavelets. In this paper, we investigate how to find and normalize point values and those of derivatives of the two-direction multiscaling functions φ and multiwavelets ψ. For finding point values, we investigate the eigenvalue approach. For normalization, we investigate the normalizing conditions for them by normalizing the zeroth continuous moment of φ. Examples for illustrating the general theory are given.