Dykstra’s algorithm employs the projectors onto two closed convex sets in a Hilbert space to construct iteratively the projector onto their intersection. In this paper, we use a duality argument to devise an extension of this algorithm for constructing the resolvent of the sum of two maximal monotone operators from the individual resolvents. This result is sharpened to obtain the construction o...

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techni...

In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...

This paper studies the question of maximizing terminal wealth from expected utility in a multidimensional jump-diffusion model. The special feature of our approach is that the investor only observes the vector of stock prices, therefore leading to a partial information framework. Using non-linear filtering and change of measure techniques, we show that the optimization problem can be rewritten ...

In [4], D. Osipov and A. Parshin developed an approach to harmonic analysis on higher dimensional local fields through categories of filtered vector spaces as in [3]. In the present paper we give a variant of this approach that behaves nicely for inductive arguments. We establish Pontryagin duality, the Fourier inversion formula, and a Plancherel formula for all dimensions. ∗This paper was writ...

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n > 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some of these examples, like the Rozansky-Witten model, are of geomet...

The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove that a Jacobi structure can be defined on the base space of a generalized Lie bialgebroid. We also show that it is possible to construct a Lie bialgebroid from ...

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...

We show that M-theory compactified on a compact Joyce 8-manifold of Spin(7)holonomy, which yields an effective theory in D = 3 with N = 1 supersymmetry, admits at some special points in it moduli space a description in terms of type IIA theory on an orientifold of compact Joyce 7-manifold of G2-holonomy. We find the evidence in favour of this duality by computing the massless spectra on both M-...

Here we prove a Poincaré Verdier duality theorem for the ominimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure. RÉSUMÉ. On démontre une dualité de Poincaré Verdier dans le cadre de la cohomologie o-minimale des faisceaux avec support compact et définissable sur un espace définissablement normaux, défin...