Titlebook: An Introduction to Frames and Riesz Bases; Ole Christensen Textbook 2016Latest edition Springer International Publishing Switzerland 2016

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Frames in Finite-Dimensional Inner Product Spaces, “elementary building blocks” and hereby helps us by reducing many questions concerning general vectors to similar questions concerning only the basis elements. However, the conditions to a basis are very restrictive – no linear dependence between the elements is possible, and sometimes we even want

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Infinite-Dimensional Vector Spaces and Sequences,nal vector spaces. Here great care is needed: we need to replace finite sequences . by infinite sequences ., and suddenly the question of convergence properties becomes a central issue. The vector space itself might also cause problems, e.g., in the sense that Cauchy sequences might not be convergen