2020/06/09 by Aurelian Bejancu, Bejancu, Aurelian
Mathematics · Physics and Astronomy · #15B05 #41A05 #41A15 #41A63 #42B05 #47A68 #47B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CA #msc:15B05 #msc:41A05 #msc:41A15 #msc:41A63 #msc:42B05 #msc:47A68 #msc:47B35
paper · pdf · doi:10.48550/arxiv.2006.05282
40 pages
arxiv created 2020/06/09 · openalex publication_date 2020/06/09 · arxiv updated 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H⊂ℤd be a half-space lattice, defined either relative to a fixed coordinate (e.g. H = ℤd-1 × ℤ+), or relative to a linear order \preceq on ℤd, i.e. H = \j∈ℤd : 0\preceq j\. We consider the problem of interpolation at the points of H from the space of series expansions in terms of the H-shifts of a decaying kernel ϕ. Using the Wiener-Hopf factorization of the symbol for cardinal interpolation with ϕ on ℤd, we derive some essential properties of semi-cardinal interpolation on H, such as existence and uniqueness, Lagrange series representation, variational characterization, and convergence to cardinal interpolation. Our main results prove that specific algebraic or exponential decay of the kernel ϕ is transferred to the Lagrange functions for interpolation on H, as in the case of cardinal interpolation. These results are shown to apply to a variety of examples, including the Gaussian, Matérn, generalized inverse multiquadric, box-spline, and polyharmonic B-spline kernels.