Almost strict total positivity and a class of Hurwitz polynomials - Dimitrov, D. K.; Pena, J. M. (Elsevier B.V., 2005)
We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.
Keywords: totally positive matrix; strictly totally positive matrix; shadows' lemma; Hurwitz polynomial; entire function in the Laguerre-Polya class