Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...

The theory of localized frames is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet frames. Using the new notion of a R-dual sequence associated with a Bessel sequence, we derive several duality principles concerning localization in abstract frame theory. As applications of our results we prove a duality princi...

This paper presents a general and complete duality theory for optimal control of systems governed by linear ordinary differential equations with a convex cost criterion. Existence theorems for optimal control problems are obtained using the duality theory and a direct relationship between duality and Pontryagin's Maximum Principle is exhibited. Finally, applications to decomposition of optimal ...

Observer design is classically considered as a dual problem to state feedback. But very few results address this issue in the context of uncertain system, at least in comparison of robust state-feedback design. This fact has motivated us for studying robust design of both state-feedback gains and Luemberger-like observers and we in particular show that in case of uncertain systems these two des...

A general abstract duality result is proposed for equations which are governed by the sum of two operators (possibly multivalued). It allows to unify a large number of variational duality principles, including the Clarke-Ekeland least dual action principle and the Singer-Toland duality. Moreover, it offers a new duality approach to some central questions in the theory of variational inequalitie...

There is a well known duality concept in propositional logic (cf. e.g. [3, 14]) essentially relating CNF formulas to tautologically equivalent DNF formulas. In this paper we propose and discuss another duality principle in propositional logic based on a set theoretic duality interchanging clauses and literals, thus working for arbitrary normal form formulas. This concept is closely related to a...