The original motivation of this paper, as presented in [15], was to compute the dual space of a lattice of subsets of some free monoid A. According to StonePriestley duality, the dual space of a lattice can be identified with the set of its prime filters, but it is not always the simplest way to describe it. Consider for instance the Boolean algebra generated by the sets of the form uA, where u...

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.

Given a frame for a subspace W of a Hilbert space H , we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a gener...

We show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. Applications are given to normed ideals of operators.

Let V →֒ H →֒ V ∗ be a normal triple of spaces with dense and continuous embeddings, where V is a reflexive Banach space, H is a Hilbert space, identified with its dual by means of the inner product in H , and V ∗ is the dual of V . Let W = (Wt)t≥0 be an r-dimensional Brownian motion carried by a stochastic basis (Ω,F , (Ft)t≥0, P ). In this paper, we study the approximation of the solution to th...

Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us ...

For a real or p-adic connected reductive group G, Harish-Chandra introduced the Plancherel measure on the tempered dual Ĝtemp and founded the Plancherel formula [7, 18] relating functions on G to functions on Ĝtemp. While the Plancherel measure is equal to the formal degree for square-integrable representations, there has been no similar interpretation for tempered but nonsquare-integrable repr...

We construct an exact regular vortex solution to the self-dual equations of the Abelian Higgs model in non-commutative space for arbitrary values of θ. To this end, we propose an ansatz which is the analogous, in Fock space, to the one leading to exact solutions for the Nielsen-Olesen vortex in commutative space. We compute the flux and energy of the solution and discuss its relevant properties.