LINEAR FORMS AND QUADRATIC UNIFORMITY FOR FUNCTIONS ON

Quadratic Functions, Optimization, and Quadratic Forms

Linear-quadratic Control and Quadratic Differential Forms

We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...

Quadratic Forms and Height Functions

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear quadratic control problem where the performance functional is the integral of a quadratic differential form. We look for characterizations of the set of stationary trajectories and of the set of local minimal traj...

Linear Forms from the Gowers Uniformity Norm

The application we have in mind is ν = p1S where S ⊆ ZN satisfies S ⊆ ZN and p = |S| /N . We do not give all the details in this note and we also assume familiarity with [1]. We sketch how to modify the argument in [1] to show the result under the assumption (1). As noted in Footnote 5 on page 16 of [1], the only hypotheses needed for the proof of the counting lemma are the strong linear forms ...