Wiener–Hopf Difference Equations and Semi-Cardinal Interpolation with Integrable Convolution Kernels

Abstract Let $$H\subset {\mathbb {Z}}^d$$ H ⊂ Z d be a half-space lattice, defined either relative to fixed coordinate (e.g. $$H = {Z}}^{d-1}\!\times \!{\mathbb {Z}}_+$$ = - 1 × + ), or linear order $$\preceq $$ ⪯ on $${\mathbb , i.e. \{j\in {Z}}^d: 0\preceq j\}$$ { j ∈ : 0 } . We consider the problem of interpolation at points H from space series expansions in terms -shifts decaying kernel $$\phi ϕ Using Wiener–Hopf factorization symbol for cardinal with we derive some essential properties semi-cardinal such as existence and uniqueness, Lagrange representation, variational characterization, convergence interpolation. Our main results prove that specific algebraic exponential decay is transferred functions case These are shown apply variety examples, including Gaussian, Matérn, generalized inverse multiquadric, box-spline, polyharmonic B-spline kernels.