SINGULARITY OF CARDINAL INTERPOLATION WITH SHIFTED BOX SPLINES Academic Article

Cardinal interpolation by integer translates of shifted box splines Mn, = Mnnn(. + ) on the three-direction mesh is studied. Let = (- 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, does not vanish on the torus T2 for all in the shift region . In this work, it is shown that the symbol of Mn, always vanishes somewhere on T2 if [- 1 2, 1 2]2. In other words the cardinal interpolation operator corresponding to Mn, , [- 1 2, 1 2]2, n = 1, 2, , is invertible if and only if . 1993 Academic Press, Inc.

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