Standard Models under Polynomial Positivity Conditions
نویسندگان
چکیده
We develop standard models for commuting tuples of bounded linear operators on a Hilbert space under certain polynomial positivity conditions, generalizing the work of V. Müller and F.-H. Vasilescu in [6], [14]. As a consequence of the model, we prove a von Neumann-type inequality for such tuples. Up to similarity, we obtain the existence of in a certain sense “unitary” dilations.
منابع مشابه
Investigation of Parameter Perturbation Region for Positive Polynomials
In this paper the robust positivity of polynomials under coefficient perturbation is investigated. This robust positivity of polynomials can be used for polynomial systems in order to determine the robust asymptotic stability of the system. It is assumed that the polynomials under investigation depend linearly on some parameters. The aim in the article is to determine the parameter perturbation...
متن کاملData Bounded Polynomials and Preserving Positivity in High Order ENO and WENO Methods
The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on s...
متن کاملTotal Positivity and Refinable Functions with General Dilation
We show that a refinable function φ with dilationM ≥ 2 is a ripplet, i.e., the collocation matrices of its shifts are totally positive, provided that the symbol p of its refinement mask satisfies certain conditions. The main condition is that p (of degree n) satisfies what we term condition (I), which requires that n determinants of the coefficients of p are positive and generalises the conditi...
متن کاملThe Incidence Class and the Hierarchy of Orbits
R. Rimányi defined the incidence class of two singularities η and ξ as [η]|ξ, the restriction of the Thom polynomial of η to ξ. He conjectured that (under mild conditions) [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η. Generalizing this notion we define the incidence class of two orbits η and ξ of a representation. We give a sufficient condition (positivity) for ξ to have the property that [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η for any ot...
متن کاملA review of the book “ Homogeneous polynomial forms for robustness analysis of uncertain systems
The book describes convex optimization techniques to deal with stability and performance evaluation for linear dynamical systems subject to parametric uncertainty. It summarizes approximately a decade of research activities, and most of the material in the book has been gathered from conference and journal publications by the authors. The originality of the authors’ approach to system robustnes...
متن کامل