Coorbit Spaces for Dual Pairs

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gr\"ochenig in the 1980's. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic decompositions can be constructed through sampling. We further present a wavelet characterization of Besov spaces on the forward light cone

Examples of Coorbit Spaces for Dual Pairs

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\"ochenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of $\mathrm{SL}_2(\mathbb{R})$. We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to c0c_0

We prove that a Hilbert space frame \fti contains a Riesz basis if every subfamily \ftj , J \subseteq I , is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements

Weyl-Heisenberg frames for subspaces of L^2(R)

We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous known conditions.Comment: 13 page

Threats to soil quality in Denmark - A review of existing knowledge in the context of the EU Soil Thematic Strategy

The EU Commission is preparing a proposal for a Soil Framework Directive with the purpose of protecting the soil resources in Europe. The proposal identifies six major threats to the sustained quality of soils in Europe. This report addresses the threats that are considered most important under the prevailing soil and climatic conditions in Denmark: compaction, soil organic matter decline, and erosion by water and tillage. For each of these threats, the relevance and damage to soil functions as well as the geographic distribution in Denmark are outlined. We suggest a procedure for identifying areas at risk. This exercise involves an explicit identification of: i) the disturbing agent (climate / management) exerting the pressures on soil, and ii) the vulnerability of the soil to those stresses. Risk reduction targets, measures required to reach these targets, and the knowledge gaps and research needs to effectively cope with each threat are discussed. Our evaluation of the threats is based on soil resilience to the imposed stresses. Subsoil compaction is considered a severe threat to Danish soils due to frequent traffic with heavy machinery in modern agriculture and forestry. The soil content of organic matter is critically low for a range of Danish soils, which should be counteracted by appropriate management options. Soil erosion by tillage, and to a lesser degree by water, adversely affects soil quality on much of the farmland because degradation rates are much higher than generation of soil

I give at the office: A review of workplace giving research, theory, and practice

Workplace giving is a widely used philanthropic tool. Although it may have great unmet potential, it is also facing a number of challenges, including competition from informal crowdfunding campaigns. In the face of such challenges, we take stock of the extant research to better understand the value and future of workplace giving, emphasizing employee actions and preferences in our review. Workplace giving studies can also augment knowledge about contextual giving or bounded settings for exploring basic philanthropic questions (e.g., donor control or gift elasticity). We use a three‐part conceptual framework to synthesize and discuss research on individual workplace giving in the context of broader giving behaviors. We address what researchers know, do not know, and need to know on the topic of workplace giving

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page