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

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

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