LAUSR

Let ? be agiven probability measure supported by a compact subset [a, b] ? R. Given a function ? element of L2([a,b],d?), we proved, under some integrability conditions, that a continuous version of ? can be pointwisely and uniformly approximated by a sequence of polynomial functions. More precisely by apartial-sum of orthogonal polynomials in L2 ([a,b],d?). As an application, we have used the obtained approximation Theorem to set up a polynomial interpolation algorithm of L2-functions. The derived interpolation algorithm has been implemented and compared to standard ones, such as the spline-cubic one.