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- W1025692197 abstract "In this chapter, we identify ideal window functions χ I on finite intervals I and time–frequency shift lattices $a {mathbb{Z}}times b{mathbb{Z}}$ such that the corresponding Gabor systems $$mathcal G(chi_I, a {mathbb{Z}}times b{mathbb{Z}}):={e^{-2pi i n bt} chi_I(t- m a): (m, n)in{mathbb{Z}}times{mathbb{Z}}}$$ are frames for $L^2({mathbb{R}})$ . Also we consider a stable recovery of rectangular signals f in a shift-invariant space shift-invariant space $$V_2(chi_I, b{mathbb{Z}}):=Big{sum_{lambdain b{mathbb{Z}}} d(lambda) chi_I(t-lambda): sum_{lambdain b{mathbb{Z}}} |d(lambda)|^2<inftyBig}$$ from their equally-spaced samples $f(t_0+mu), muin a{mathbb{Z}}$ , for arbitrary initial sampling sampling position t 0." @default.
- W1025692197 created "2016-06-24" @default.
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- W1025692197 date "2015-01-01" @default.
- W1025692197 modified "2023-09-23" @default.
- W1025692197 title "The abc-Problem for Gabor Systems and Uniform Sampling in Shift-Invariant Spaces" @default.
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- W1025692197 doi "https://doi.org/10.1007/978-3-319-13230-3_8" @default.
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