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Titlebook: Excursions in Harmonic Analysis, Volume 1; The February Fourier Travis D. Andrews,Radu Balan,Kasso A. Okoudjou Book 2013 Springer Science+B

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Excursions in Harmonic Analysis, Volume 1978-0-8176-8376-4Series ISSN 2296-5009 Series E-ISSN 2296-5017
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Unions of Subspaces for Data Modeling and Subspace Clusteringnear subsets can also serve as signal model, e.g., signals with finite rate of innovation or sparse signals. Discovering the model from data observations is a fundamental task. The goal of this chapter is to discuss the problem of learning a nonlinear model of the form . from a set of observations .
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Fusion Frames and Unbiased Basic Sequenceson of similar types of fusion frames is even less developed. We construct a large family of equi-isoclinic Parseval fusion frames by taking the Naimark complement of the union of orthonormal bases. If these bases are chosen to be mutually unbiased, then the resulting fusion frame subspaces are spann
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Sampling in Spaces of Bandlimited Functions on Commutative Spacesrable functions on . is commutative. In this chapter we introduce the space . of .-bandlimited function on . by using the spectral decomposition of .. We show that those spaces are reproducing kernel Hilbert spaces and determine the reproducing kernel. We then prove sampling results for those spaces
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A Panorama of Sampling Theoryis an orbit . of a countable abelian group . acting continuously on ., and each .∈. is the sum of the terms ., .. Such a recovery formula generalizes the well-known Shannon sampling formula. This chapter presents a general discussion of sampling theory and introduces several new classes of sampling
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