Zero-diminishing linear transformations

Craven, Thomas; Csordas, George

doi:10.1090/S0002-9939-1980-0587923-5

Zero-diminishing linear transformations
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by Thomas Craven and George Csordas PDF

Proc. Amer. Math. Soc. 80 (1980), 544-546 Request permission

Abstract:

This paper solves an open problem of Karlin. We consider linear transformations defined on the set of all polynomials with real coefficients and give a complete characterization of the transformations with the property that they maintain or reduce the number of real zeros of each polynomial.

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