Some New Results on the Qualitative Theory of Generalized Polynomials
John Maroulas, Stephen Mark Barnett · IMA Journal of Applied Mathematics · 1978
A polynomial is termed generalized when it is expressed in terms of an arbitrary orthogonal basis. A number of classical results on the qualitative analysis of polynomials in power form are extended to the generalized case. In particular, a Routh-type tabular array, and a Sylvester-type matrix are derived, for determining the greatest common divisor of two polynomials in generalized form. This leads to an analogue of the Routh-Hurwitz criteria for stability and zero location of a generalized polynomial. A number of related applications of the techniques are also discussed.