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

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COKE

Die Technik der Blutgruppenuntersuchung,The previous chapters have concentrated on general frame theory. We have only seen a few concrete frames, and most of them were constructed via manipulations on an orthonormal basis for an arbitrary separable Hilbert space. An advantage of this approach is that we obtain universal constructions, valid in all Hilbert spaces.

興奮過度

https://doi.org/10.1007/978-3-642-80492-2A fundamental question in wavelet analysis is what conditions we have to impose on a function . such that a given signal . can be expanded via translated and scaled versions of ., i.e., via functions

巨頭

,Technik und Ph?nomenologie der Hypnose,In this chapter we consider .,i.e., wavelet systems for . with scaling parameter .?=?2 and translation parameter .?=?1.?We will usually denote the resulting wavelet systems . by . or . Recall that bases of this type were considered already in Section?.

FLASK

Schwachsinnig oder schwer erziehbar?,The introduction of multiresolution analysis by Mallat and Meyer was the beginning of a new era; the short descriptions in Section?. and Section?. only give a glimpse of the research activity based on this new tool, aiming at construction of orthonormal bases .

魯莽

Die Technik der IndividualpsychologieFrame multiresolution analysis is just one way to construct wavelet frames via multiscale techniques. We already mentioned in Section?. that the conditions can be weakened further, and the purpose of this chapter is to show how one can still construct frames.

北極人

Bases and Their Limitations,The next chapters will deal with generalizations of the basis concept, so it is natural to ask why they are needed. Bases exist in all separable Hilbert spaces and in practically all Banach spaces of interest, so why do we have to search for generalizations?

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