IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## Some Remarks on Zero-Increasing Transformations

• Sept. 12, 2000
• 3:30 p.m.
• LeConte 312

## Abstract

Let T be a linear operator which maps polynomials of degree n to polynomials of degree n , for every n . We discuss the problem of trying to characterize the set of all such operators which satisfy

$Z _ I(p) \le Z _ J(Tp)$

for every real-valued polynomial p , where $Z _ I$ counts the number of zeros on the interval I of ℝ.

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