Local energy integrals for effectively hyperbolic operators I

Quantum Energy Inequalities and Local Covariance I: Globally Hyperbolic Spacetimes

We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covari-ance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions. Local covariance permits us to place constraints on the renormalised stress-energy tensor in one spacetime using QEIs derived in another, in subregions where...

Hyperbolic Beta Integrals

Hyperbolic beta integrals are analogues of Euler’s beta integral in which the role of Euler’s gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q̃ )-bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q| = 1. The integrals under considerat...

Representation of Feedback Operators for Hyperbolic Systems

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numeric...

Representation Of Feedback Operators For Hyperbolic Systems

Generalized local operators between function modules

Let X be a compact Hausdorff space, E be a normed space, A(X,E)  be a regular Banach function algebra on X , and A(X,E) be a subspace of C(X,E) . In this paper, first we introduce the notion of localness of an additive map S:A(X,E) → C(X,E) with respect to  additive maps T1,...,Tn: A(X) → C(X) and then we characterize the general form of such maps for a certain class of subspaces A(X,E) of C(...