Operators in Rigged Hilbert spaces: some spectral properties

A notion of resolvent set for an operator acting in a rigged Hilbert space \D \subset \H\subset \D^\times is proposed. This set depends on a family of intermediate locally convex spaces living between \D and \D^\times, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.Comment: 29 page

Framework for Static and Dynamic Friction Identification for Industrial Manipulators

Even if friction modeling and compensation is a very important issue for manipulators, quite simple models are often adopted in the industrial world to avoid too heavy solutions from the computational point of view, and because of the difficulty of finding and identifying a model applicable in any motion condition. This article proposes a general framework for friction identification for industrial manipulators with the goal of solving the previous problems through: first, a complete procedure managing all the steps from data acquisition and model identification up to the generation of the code for the implementation into the robot software architecture, second, the possibility of adopting static or dynamic models of different complexity, and third, the development of some modifications in the dynamic friction model so to achieve a reliable friction torque estimation at any velocity and acceleration regime, avoiding unfeasible peaks and overestimation. The results of experimental tests carried out for different manipulators prove the validity and generality of the proposed friction model and identification procedure

The pluricomplex Poisson kernel for strongly convex domains

Let D be a bounded strongly convex domain in the complex space of dimension n. For a fixed point p epsilon partial derivative D, we consider the solution of a homogeneous complex Monge-Ampere equation with a simple pole at p. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of D with pole at p. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of D, uniqueness in terms of the associated foliation and boundary behaviors. Finally, using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

Common stochastic trends and aggregation in heterogeneous panels

In nonstationary heterogeneous panels where the number of units is finite and where each unit cointegrates, a large number of conditions needs to be satisfied for cointegration to be preserved in the aggregate relationship. In reality, the conditions most likely will not hold. This paper takes a closer look at what happens when the conditions are violated. In this case, the question of whether an aggregate relationship is observationally equivalent to a cointegrating equation is of particular interest. We derive a measure of the degree of noncointegration of the aggregate estimates, and we explore its asymptotic properties

Maximal extensions of a linear functional

Extensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A0 of a topological *-algebra A[τ] are analyzed. It turns out that their maximal extensions as linear functionals or hermitian linear functionals are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [2] is revisited from this point of view. Examples mostly taken from the theory of integration are discussed

SVEP and local spectral radius formula for unbounded operators

In this paper we study the localized single valued extension property for an unbounded operator T. Moreover, we provide sufficient conditions for which the formula of the local spectral radius holds for these operators