We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space C or the fractional Sobolev space L , then the superspace can be chosen to be C or L , re...

We consider locally defined operators of the form D ◦K where D is the operator of differentiation and K maps the space of continuous functions into the space of n-times differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed.

The local reconstruction from samples is one of most desirable properties for many applications in signal processing, but it has not been given as much attention. In this paper, we will consider the local reconstruction problem for signals in a shiftinvariant space. In particular, we consider finding sampling sets X such that signals in a shift-invariant space can be locally reconstructed from ...

Introduction. In [l] L. Markus and the author introduced the concept of holonomy covering spaces for flat affinely connected manifolds or what are also called locally affine spaces. We also proved in [l ] that the holonomy covering space of a complete « dimensional locally affine space must be some « dimensional cylinder, i.e., T^XF"-*, i = 0, •■-,«, where T* denotes the locally affine i dimens...

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces in some Euclidean space that are locally bi-Lipschitz equivalent to an open subset of the plane.

We extend the basic results on the theory of the generalized Riemann integral to the setting of bounded or locally nite measures on locally compact second countable Hausdorr spaces. The correspondence between Borel measures on X and continuous valuations on the upper space UX gives rise to a topological embedding between the space of locally nite measures and locally nite continuous valuations,...

We consider the estimation of acoustic impulse responses from the simultaneous recording of several known sources. Existing techniques are restricted to the case where the number of sources is at most equal to the number of sensors. We relax this assumption in the case where the sources are known. To this aim, we propose statistical models of the filters associated with a convex log-likelihood,...

A locally truncated geometry with diagram of type affine E7 is studied. One considers a parapolar space e Γ, locally of type A7,4, which is subject to an extra axiom. A covering Γ of this space is constructed. It is proved that Γ is a rank 6, residually connected, locally truncated diagram geometry which is a homomorphic image of a truncated building of affine type E7. Consequently, e Γ is also...

A k-triangulation of a convex polygon is a maximal set of diagonals so that no k + 1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a convex n-gon and pairs of non-crossing Dyck paths of length 2(n−4). This gives a bijective proof of a recent result of Jonsson for the case k = 2. We obtain the bijection by constructing isomorphic generating trees f...

RÉSUMÉ. Cet article présente une approche de résolution des problèmes d’optimisation multicritères basant su l’outil LMI. Notre objectif est de chercher un contrôleur stabilisant le système avec des contraintes fréquentielles et/ou temporelles. Cette conception est fondée sur la paramétrisation de Youla; cette paramétrisation est basée sur un contrôleur initial défini par la combinaison convexe...