Singularity of Cardinal Interpolation with Shifted Box Splines Academic Article uri icon

abstract

  • Cardinal interpolation by integer translates of shifted box splines Mn, ω = Mnnn(. + ω) on the three-direction mesh is studied. Let Λ = (- 1 2, 1 2)2 ⋂ ((s, t): |s - t| < 1 2). In a previous work by these authors it was shown that the symbol of Mn, ω does not vanish on the torus T2 for all ω in the shift region Λ. In this work, it is shown that the symbol of Mn, ω always vanishes somewhere on T2 if ω ϵ [- 1 2, 1 2]2Λ. In other words the cardinal interpolation operator corresponding to Mn, ω, ω ϵ [- 1 2, 1 2]2, n = 1, 2, …, is invertible if and only if ω ϵ Λ. © 1993 Academic Press, Inc.

author list (cited authors)

  • Chui, C. K., Stockler, J., & Ward, J. D.

citation count

  • 2

publication date

  • August 1993