Non-negativity, polynomials, exponential functions, trigonometric polynomials, generalized Budan-Fourier sequence, Kronecker's approximation theorem, Lipschitz continuity
This paper concerns the class of functions that are solutions of homogeneous linear differential equations with constant real coefficients. This class, which is ubiquitous in the mathematical sciences, is denote by EPT. We present necessary conditions and a new sufficient condition for non-negativity of such an EPT function on the half-line. We obtain a sufficient condition for an EPT function to be non-negative on an unbounded subinterval of [0,infinity). The completion of the analysis is reliant on a generalized Budan-Fourier technique, devised by the authors, to determine the non-negativity of an EPT function on the complementary finite interval.
W. Arendt, J.A. Ball,J. Behrndt, K-H Foerster, V. Mehrmann, C. Trunk