Semi-infinite cardinal interpolation with multiquadrics and beyond

This paper concerns the interpolation with radial basis functions on half-spaces, where the centres are multi-integers restricted to half-spaces as well. The existence of suitable Lagrange functions is shown for multiquadrics and inverse multiquadrics radial basis functions, as well as the decay rate and summability of its coefficients. The main technique is a so-called Wiener-Hopf factorisation of the symbol of the radial basis function and the careful study of the smoothness of its 2 pi-periodic factors.