## 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.