Book Chapter Details
Mandatory Fields
B. Hanzon and F. Holland
2012 Unknown
Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations
Non-negativity Analysis for Exponential-Polynomial-Trigonometric Functions on [0,infinity)
Optional Fields
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
Grant Details
Science Foundation Ireland
SFI grant numbers RFP2007-MATF802; 07/MI/008.