On the Remainders and the Convergence of Cardinal Spline Interpolation for Almost Periodic Functions

摘要: Remainders in terms of high-order derivatives might at times seem rather useless for numerical applications. However, they are often effective theoretical problems convergence. Our present topic is the remainder cardinal spline interpolation (C.S.I.) odd degree 2m-1, its customary Peano form. Its kernel K2m-1(x,t) appears to be endowed with numerous worthwhile properties some which described first half (Part I) this paper. The C.S.I. allows us discuss behavior interpolant, as m → ∞, entire functions exponential type (Theorem 6 §6).