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

Two-direction multiscaling functions $\mathit{\varphi }$ and two-direction multiwavelets $\mathit{\psi }$ associated with $\mathit{\varphi }$ 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 $\mathit{\varphi }$ and multiwavelets $\mathit{\psi }$. %associated with $\mathit{\varphi }$. 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 $\mathit{\varphi }$. Examples for illustrating the general theory are given.