ScienceAsia 23 (1997): 035-040 |doi: 10.2306/scienceasia1513-1874.1997.23.035

CHARACTERIZING DISCRETE EXPONENTIAL POLYNOMIALS BY CASORATI'S DETERMINANTS

VICHIAN LAOHAKOSOL

ABSTRACT:

For a real and sufficiently smooth function f, Karlin and Loewner proved two interesting results which say roughly that
      (i) f is an exponential polynomial if and only if certain Wronskian vanishes;
      (ii) f is an exponential sum with positive coefficients if a Wronskian of certain order vanishes, while those of lower orders have the same positive sign at one point.
      We give a slightly different proof of (ii) and obtain analogues of both results in the discrete setting, with Casorati's determinants taking the place of Wronskians.

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Department of Mathematics, Kasetsart University, Bangkok 10900, Thailand.

Received November 2, 1996