Frame analysis and approximation in reproducing kernel Hilbert spaces

Details Frame analysis and approximation in reproducing kernel Hilbert spaces Frame analysis and approximation in reproducing kernel Hilbert spaces

2006-03-28

arxiv.org/abs/math/0603661v1

Mathematics

Classical Analysis and ODEs

19 pages, AMS-LaTeX, 2 figures with 4 EPS graphics

Scientific paper

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building on a geometric formula for the analysis operator defined from F. Our focus is on the infinite-dimensional case where a priori estimates play a central role, and we extend a number of results which are known so far only in finite dimensions. We further show how this approach may be used both in constructing useful frames in analysis and in applications, and in understanding their geometry and their symmetries.

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