On Almost Everywhere Convergence of Tensor Product Spline Projections
On Almost Everywhere Convergence of Tensor Product Spline Projections
Let d∈N, and let f be a function in the Orlicz class L(log+L)d−1 defined on the unit cube [0,1]d in Rd. Given knot sequences Δ1,…,Δd on [0,1], we first prove that the orthogonal projection P(Δ1,…,Δd)(f) onto the space of tensor product splines with arbitrary orders (k1,…,kd) and knots Δ1,…,Δd converges …