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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Zero-diminishing linear transformations


Authors: Thomas Craven and George Csordas
Journal: Proc. Amer. Math. Soc. 80 (1980), 544-546
MSC: Primary 12D10; Secondary 30C15
MathSciNet review: 587923
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0587923-5
Keywords: Zero-diminishing transformation, polynomial, number of real zeros, entire function, exponential polynomial
Article copyright: © Copyright 1980 American Mathematical Society