Record number :
851064
Title of article :
Singularity of Cardinal Interpolation with Shifted Box Splines Original Research Article
Author/Authors :
C.K. Chui، نويسنده , , J. Stockler، نويسنده , , J.D. Ward، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1993
Pages :
29
From page :
123
To page :
151
Abstract :
Cardinal interpolation by integer translates of shifted box splines Mn, ω ≔ Mnnn(· + ω) on the three-direction mesh is studied. Let Λ ≔ (−12, 12)2 ∩ {(s, t) : |s − t| < 12}. 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 ∈ [−12, 12]2\Λ. In other words the cardinal interpolation operator corresponding to Mn, ω, ω ∈ [−12, 12]2, n = 1, 2, ..., is invertible if and only if ω ∈ Λ.
Journal title :
Journal of Approximation Theory
Serial Year :
1993
Link To Document :
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