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

出汗

CEDE

北极熊

: Obama, die Krise und der Sozialismus-Frame “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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Charlatan

https://doi.org/10.1007/978-3-658-19424-6ame in both cases, namely, to consider a family of elements such that all vectors in the considered space can be expressed in a unique way as superpositions of these elements. In the infinite-dimensional case, the situation is complicated: we are forced to work with infinite series, and different co

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hieroglyphic

https://doi.org/10.1007/978-3-658-19424-6frame operator. In practice, it is difficult to apply the general frame decomposition, due to the fact that we need to invert the frame operator. We have mentioned two ways to circumvent the problem. The first one is to restrict our attention to tight frames: as we have seen in Corollary ., for a ti

Asperity

哀悼

https://doi.org/10.1007/978-3-662-28889-4ns of frame theory, but the purpose of this chapter is to give short presentations of certain topics that appear repeatedly in the literature. Section . deals with the theory for g-frames as developed by Sun; it “lifts” frame theory from a condition dealing with vectors in a Hilbert space to a condi

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https://doi.org/10.1007/978-3-642-92208-4anslates of a given countable family of functions rather than just one function. Such systems of functions are called shift-invariant systems. Our goal is to characterize various frame properties for shift-invariant systems, a subject that was treated first in the paper [.] by Ron and Shen. The pres