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Perhaps the most useful analytic tool in gauge theory is the Uhlenbeck compactness theoremfor sequences of unitary connections on hermitian vector bundles [U]. Given connections {Dj} ona bundle E over...
Frames which are tight might be considered optimally conditioned in the sense of their numerical stability.This leads to the question of perfect preconditioning of frames,i.e., modification of a given...
Finite frames can be viewed as mass points distributed in N-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic fram...
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames.These are (finite) frames with the property that e...
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight...
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of pri...
We show that multi-window Gabor frames with windows in the Wiener algebra W(L∞, `1) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove thecanonical dual of a Gabo...
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight...
A finite collection of unit vectors S ⊂ Rn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We p...
The objective of this paper is the linear reconstruction of a vector, up to a unimodular constant, when all phase information is lost, meaning only the magnitudes of frame coefficients are known. Reco...
In this paper we present a signal reconstruction algorithm from absolute value of frame coefficients that requires arelatively low redundancy. The basic idea is to use a nonlinear embedding of the inp...
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type co...
The excess of a sequence in a Hilbert space is the greatest number of elements that can be removed yet leave a set with the same closed span. We study the excess and the dual concept of the deficit of...
Frames have applications in numerous fields of mathematics and engineering.The fundamental property of frames which makes them so useful is their overcompleteness.In most applications, it is this over...
This work develops a quantitative framework for describing the overcompleteness of a large class of frames. A previous article introduced notions of localization and approximation between two frames F...

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