Abstra ct. Positive real rational functions play a central role in both deterministic and stochastic linear systems theory, arising in circuit synthesis, filtering, interpolation, spectral analysis, speech processing, stability theory, stochastic realization theory and systems identification – to name just a few. For this reason, results about positive real transfer functions and their realizat...

In this paper, a pair of multiobjective fractional variational symmetric dual problems over cones is formulated. Weak, strong and converse duality theorems are established under generalized F-convexity assumptions. Moreover, self duality theorem is also discussed. 2007 Elsevier B.V. All rights reserved.

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...

In this note we improve and extend duality theorems for crossed products obtained by M. Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case of an arbitrary Noetherian commutative ground rings under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary Noetherian ground rings.

An approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin’s duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.

Generalizing Duality Theorem of V. V. Fedorchuk [11], we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous skeletal maps, the quasi-open perfect maps, the open maps, the open perfect maps. In particular, a Stone-type duality theorem for the category of all c...