Multiplier sequences and logarithmic mesh

Details Multiplier sequences and logarithmic mesh Multiplier sequences and logarithmic mesh

2010-10-28

arxiv.org/abs/1010.6052v1

Mathematics

Classical Analysis and ODEs

5 pages, no figures

Scientific paper

In this note we prove a new result about (finite) multiplier sequences, i.e. linear operators acting diagonally in the standard monomial basis of R[x] and sending polynomials with all real roots to polynomials with all real roots. Namely, we show that any such operator does not decrease the logarithmic mesh when acting on an arbitrary polynomial having all roots real and of the same sign. The logarithmic mesh of such a polynomial is defined as the minimal quotient of its consecutive roots taken in the non-decreasing order.

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