On the zeros of derivatives of balanced trigonometric polynomials

Carl L. Prather

Vol. 81 (1979), No. 2, 515–523

DOI: 10.2140/pjm.1979.81.515

Abstract

The final set and initial set for a balanced 2π-periodic trigonometric polynomial with roots in a horizontal strip are obtained. Assuming the limits have finite order, we show that only trigonometric polynomials are uniform limits on compact sets of balanced 2π-periodic trigonometric polynomials that have only real zeros. The final set result is extended to balanced almost periodic trigonometric polynomials. Finally, we give a final set result for balanced exponential sums whose exponents are complex.

Mathematical Subject Classification 2000

Primary: 42A05

Secondary: 30C15, 42A75

Milestones

Received: 21 November 1977

Revised: 17 October 1978

Published: 1 April 1979