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The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the $1960$'s, by exploiting a "miracle": a certain naturally appearing integral operator commutes with an explicit differential one.
Prolate spheroidal wave functions, Fourier analysis and uncertainty. II
H. J. Landau and H. O. Pollak · 1961
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Prolate spheroidal wave functions, Fourier analysis and uncertainty. I
D. Slepian and H. O. Pollak · 1961
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Prolate spheroidal wave functions, Fourier analysis and uncertainty. III. The dimension of the space of essentially time- and band-limited signals
H. J. Landau and H. O. Pollak · 1962
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Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions
D. Slepian · 1964
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Prolate spheroidal wave functions, Fourier analysis and uncertainty. V
H. J. Landau and H. O. Pollak · 1978
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Convolution algorithms for arbitrary projections angles
M. E. Davison and F. A. Grünbaum · 1979
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Tomographic reconstruction with arbitrary directions
M. E. Davison and F. A. Grünbaum · 1981
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Differential operators commuting with finite convolution integral operators: some nonabelian examples
F. A. Grünbaum, L. Longhi, and M. Perlstadt · 1982
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V. Katsnelson and R. Machluf · 2012
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Tensor tomography: Progress and challenges
G. P. Paternain, M. Salo, and G. Uhlmann · 2014
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Spherical functions of fundamental K K -types associated with the n n -dimensional sphere
J. Tirao and I. Zurrián · 2014
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The Darboux process and time-and-band limiting for matrix orthogonal polynomials
M. Castro and F.A. Grünbaum · 2015
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SIGMA, Symmetry Integrability Geom. Methods Appl
F. A. Grünbaum, I. Pacharoni, and I. Zurrián · 2015
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