Perturbed Hilbert-Schmidt frames remain frames under quantitative stability criteria that depend on perturbation size and the number of changed elements for finite cases, and on global control for infinite cases.
M.: An Introduction to Nonharmonic Fourier Series
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Sufficient conditions are derived for sums of Weyl-Heisenberg frames to form frames for L2(R), including infinite sums under convergence of square-root upper bounds, and these are applied to accelerate the frame algorithm.
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On perturbation of Hilbert-Schmidt frames
Perturbed Hilbert-Schmidt frames remain frames under quantitative stability criteria that depend on perturbation size and the number of changed elements for finite cases, and on global control for infinite cases.
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Sums of Frames from the Weyl--Heisenberg Group and Applications to Frame Algorithm
Sufficient conditions are derived for sums of Weyl-Heisenberg frames to form frames for L2(R), including infinite sums under convergence of square-root upper bounds, and these are applied to accelerate the frame algorithm.