Let p, n ∈ ℕ with 2p ≥ n + 2, and let I a be a polyharmonic spline of order p on the grid ℤ × aℤ n which satisfies the interpolating conditions
for j ∈ ℤ, m ∈ ℤ n where the functions d j : ℝ n → ℝ and the parameter a > 0 are given. Let
be the set of all integrable functions f : ℝ n → ℂ such that the integral
The main result states that for given
there exists a constant c>0 such that whenever
j ∈ ℤ, satisfy
for all j ∈ ℤ there exists a polyspline S : ℝ n+1 → ℂ of order p on strips such that
for all y ∈ ℝ n , t ∈ ℝ and all 0 < a ≤ 1.