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 کاملClasses of Finite Equal Norm Parseval Frames
Finite equal norm Parseval frames are a fundamental tool in applications of Hilbert space frame theory. We will derive classes of finite equal norm Parseval frames for use in applications as well as reviewing the status of the currently known classes.
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...
متن کاملMoving Parseval Frames for Vector Bundles
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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ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2020
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-020-00372-4