منابع مشابه
On Fourier Frames
We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges’ theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a cla...
متن کاملComp760, Lectures 4-5: Fourier Uniformity
Blum, Luby, and Rubinfeld [1] made a beautiful observation that given a function f : Z2 → Z2, it is possible to inquire the value of f on a few random points, and accordingly probabilistically distinguish between the case that f is a linear function and the case that f has to be modified on at least > 0 fraction of points to become a linear function. Inspired by this observation, Rubinfeld and ...
متن کاملQuantitative Measures of the Uniformity of Ceramics
The introduction of computerized recording and measurement of archaeological ceramic vessels opens new channels of research, some of which we introduce and discuss in the present contribution. In particular, we show that the accurate measurements of wheel produced pottery provide information on the deviations from the ideal cylindrical symmetry which are due to faults in various stages of the p...
متن کاملGeneralized Fourier Frames in Terms of Balayage
Based on Beurling’s theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient complexity to warrant new examples generally, and to resurrect the formulation of balayage in terms of covering criteria with an eye towards an expanded theory as w...
متن کاملOn Characterizations of Fourier Frames and Tilings
for all f ∈ H.A and B are called frame bounds.The sequence is called a tight frame if A = B. The sequence is called Bessel if the second inequality above holds. In this case, B is called the Bessel bound. Frames were first introduced by Duffin and Schaeffer [1] in the context of nonharmonic Fourier series, and today they have applications in a wide range of areas. A frame can be considered as a...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2014
ISSN: 0001-8708
DOI: 10.1016/j.aim.2013.11.012