Linear combinations of frame generators in systems of translates

A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates form a frame for $V$. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different to the recently studied case when the property to be a frame is not required.Comment: 13 pages, To appear in J. Math. Anal. App

An Approximation Problem in Multiplicatively Invariant Spaces

Let $\mathcal{H}$ be Hilbert space and $(\Omega,\mu)$ a $\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $L^2(\Omega, \mathcal{H})$ that are invariant under point-wise multiplication by functions in a fix subset of $L^{\infty}(\Omega).$ Given a finite set of data $\mathcal{F}\subseteq L^2(\Omega, \mathcal{H}),$ in this paper we prove the existence and construct an MI space $M$ that best fits $\mathcal{F}$, in the least squares sense. MI spaces are related to shift invariant (SI) spaces via a fiberization map, which allows us to solve an approximation problem for SI spaces in the context of locally compact abelian groups. On the other hand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into an orthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces. Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we also solve our approximation problem for this class of SI spaces. Finally we prove that translation invariant spaces are in correspondence with totally decomposable MI spaces.Comment: 18 pages, To appear in Contemporary Mathematic

Classifying Cantor Sets by their Fractal Dimensions

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.Comment: 10 pages, revised version. To appear in Proceedings of the AMS

Evaluación preliminar de la regeneración natural de Pinus elliottii Engelm, en Gualeguaychú, provincia de Entre Ríos

p.219-227Es ampliamente conocida la importancia de la especie Pinus elliottii como componente de forestaciones comerciales en Argentina. Existen varios antecedentes que evidencian la capacidad de regeneración natural de la misma, en diversas áreas del país. Se analizaron diferentes situaciones, observadas en una forestación de aproximadamente 3000 ha, ubicadas en cercanías de la localidad de Gualeguaychú (Entre Ríos), la cual presentaba una variada gama de edades. Se observó regeneración natural con diverso grado de desarrollo y uniformidad, bajo dosel y sin cobertura arbórea. El trabajo incluye un estudio sobre la dinámica de la regeneración bajo dosel en brinzales, y una caracterización estructural de rodales restablecidos, en condiciones de ser aprovechados comercialmente. Al estado de brinzal se registraron densidades del orden de 46 a 86 pl-m2, con diámetros a la altura del cuello entre 1,5 y 16,5 mm, y alturas entre 15 y 125 cm. Rodales restablecidos de 15 años de edad presentaron 1867 pl-ha, con un diámetro promedio (DPR) de 20,47 cm. altura del árbol tipo de 15,20 m. Siendo el volumen total c-c- de 551 m3-h

Recent Developments in Real and Harmonic Analysis: In Honor of Carlos Segovia

Featuring a collection of invited chapters dedicated to Carlos Segovia, this volume examines the developments in real and harmonic analysis. It includes topics such as: Vector-valued singular integral equations; Harmonic analysis related to Hermite expansions; Gas flow in porous media; and, Global well-posedness of the KPI Equatio