Scaling function
= Scaling function
{title2=$\varphi$}
A scaling function generates the approximation space $V_0$ of a <multiresolution analysis> by its integer translates. In an orthonormal construction those translates form an <orthonormal basis>, and $\varphi_{j,k}(x)=2^{j/2}\varphi(2^jx-k)$ generate $V_j$. Integrable orthonormal <scaling functions> have $|\widehat\varphi(0)|=1$, as follows from density and the <MRA projection Fourier identity>.