The Douglas-Rachford algorithm is widely used in sparse signal processing for minimizing a sum of two convex functions. In this paper, we consider the case where one of the functions is weakly convex but the other is strongly convex so that the sum is convex. We provide a condition that ensures the convergence of the same Douglas-Rachford iterations, provided that the strongly convex function i...

The Douglas–Rachford and Peaceman–Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract re...

For a connected open subset of the plane and n a positive integer, let B () be the space introduced by Cowen and Douglas. In this article we study the n spectrum of restrictions of T in order to obtain more information about the invariant subspaces of T. When n=l and T e Bl(fl) such that o(T) is a spectral set for T we use the functional calculus we have developed for such operators to give som...

This paper investigates the informational requirements of resource allocation processes in public goods economies with any number of firms and commodities. We show that the Lindahl mechanism is informationally efficient in the sense that it uses the smallest message space among smooth resource allocation processes that are informationally decentralized and realize Pareto optimal allocations ove...

Under consideration is the large body of signal recovery problems that can be formulated as the problem of minimizing the sum of two (not necessarily smooth) lower semicontinuous convex functions in a real Hilbert space. This generic problem is analyzed and a decomposition method is proposed to solve it. The convergence of the method, which is based on the Douglas-Rachford algorithm for monoton...

This note focuses on the coupling of a type IIA D2-brane to a background B field. It is shown that the D0-brane charge arising from the integral over the D2-brane of the pullback of the B field is cancelled by bulk contributions, for a compact D2-brane wrapping a homotopically trivial cycle in space-time. In M-theory this cancellation is a straightforward consequence of momentum conservation. T...

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism of the square onto the element. It is known that for affine...

We have analyzed the genetic basis for T cell recognition of an endogenous major histocompatibility complex class II-restricted self peptide. Transgenic mice expressing the influenza virus PR8 hemagglutinin I-Ed-restricted determinant $1 (HA Tg mice) mediate negative selection ofPR8 Sl-specific T cells, but respond to immunization with a virus containing a closely related analogue, $1(Kl13). Se...