منابع مشابه
Excess of Parseval Frames
The excess of a sequence in a Hilbert space H is the greatest number of elements that can be removed yet leave a set with the same closed span. This paper proves that if F is a frame for H and there exist infinitely many elements gn ∈ F such that F \ {gn} is complete for each individual n and if there is a uniform lower frame bound L for each frame F \ {gn}, then for each ε > 0 there exists an ...
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We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new optimal expansion for fractional OrnsteinUhlenbeck processes is derived.
متن کاملA Fundamental Identity for Parseval Frames
Frames are an essential tool for many emerging applications such as data transmission. Their main advantage is the fact that frames can be designed to be redundant while still providing reconstruction formulas. This makes them robust against noise and losses while allowing freedom in design (see, for example, [5, 10]). Due to their numerical stability, tight frames and Parseval frames are of in...
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Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a Parseval frame for a fixed Hilbert space to that of a moving Parseval frame for a vector bundle over a manifold. Many vector bundles do not have a moving ba...
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In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2009
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2008.11.017