Neutral FDE canonical representations of hyperbolic systems

Preservation of Stability under Approximation for a Neutral Fde

We consider solution semigroups associated with a linear scalar neutral equation on weighted product spaces. We select the weight function to guarantee optimal, or close to optimal, growth rate estimates on the semigroup. Then we show that the so-calledàveraging' approximation scheme preserves these growth rate estimates of the original system, uniformly in the discretization parameter.

Canonical State Representations and Hilbert Functions of Multidimensional Systems

Uniqueness of Polynomial Canonical Representations

Abstract. Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respectively. In this extended abstract we study the non-linear functional equation P (z) = Q(y(z)), where y(z) is restricted to be analytic in a neighborhood of z = 0. We provide sufficient conditions to ensure that all the roots of Q(y) are contained within the range of y(z) as well as to ha...

Hermitian Determinantal Representations of Hyperbolic Curves

(1) f = det(xM1 + yM2 + zM3), where M1,M2,M3 are Hermitian d × d matrices. The representation is definite if there is a point e ∈ R for which the matrix e1M1+e2M2+e3M3 is positive definite. This imposes an immediate condition on the projective curve VC(f). Because the eigenvalues of a Hermitian matrix are real, every real line passing through e meets this hypersurface in only real points. A pol...

Exponential Representations of the Canonical Commutation Relations

A class of representations of the canonical commutation relations is investigated. These representations, which are called exponential representations, are given by explicit formulas. Exponential representations are thus comparable to tensor product representations in the sense that they provide the possibility of computing useful criteria concerning various properties. In particular, they are ...