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A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
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Cited by 631 (64 self)
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algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finitedimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result
in finitedimensional phase spaces
, 805
"... An alternative theoretical framework for quantum spin tunneling ..."
FINITEDIMENSIONALITY OF THE SPACE OF CONFORMAL BLOCKS
, 1994
"... Abstract. Without using Gabber’s theorem, the finitedimensionality of the space of conformal blocks in the WessZuminoNovikovWitten models is proved. §0 Introduction. Conformal field theory with nonabelian gauge symmetry, called the WessZuminoNovikovWitten (WZNW) model, has been studied by ma ..."
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Abstract. Without using Gabber’s theorem, the finitedimensionality of the space of conformal blocks in the WessZuminoNovikovWitten models is proved. §0 Introduction. Conformal field theory with nonabelian gauge symmetry, called the WessZuminoNovikovWitten (WZNW) model, has been studied
Noncommutative FiniteDimensional Manifolds  I. SPHERICAL MANIFOLDS AND RELATED EXAMPLES
, 2001
"... We exhibit large classes of examples of noncommutative finitedimensional manifolds which are (nonformal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative threedimensional spherical manifolds, a noncommutative version of the sphere S 3 d ..."
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Cited by 125 (15 self)
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We exhibit large classes of examples of noncommutative finitedimensional manifolds which are (nonformal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative threedimensional spherical manifolds, a noncommutative version of the sphere S 3
HYPERREFLEXIVITY OF FINITEDIMENSIONAL SUBSPACES
"... Abstract. We show that each reflexive finitedimensional subspace of operators is hyperreflexive. This gives a positive answer to a problem of Kraus and Larson. We also show that each n– dimensional subspace of Hilbert space operators is [ √ 2n]–hyperreflexive. 1. ..."
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Cited by 4 (1 self)
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Abstract. We show that each reflexive finitedimensional subspace of operators is hyperreflexive. This gives a positive answer to a problem of Kraus and Larson. We also show that each n– dimensional subspace of Hilbert space operators is [ √ 2n]–hyperreflexive. 1.
Sampling theorems for signals from the union of finitedimensional linear subspaces
 IEEE Trans. on Inform. Theory
, 2009
"... Compressed sensing is an emerging signal acquisition technique that enables signals to be sampled well below the Nyquist rate, given that the signal has a sparse representation in an orthonormal basis. In fact, sparsity in an orthonormal basis is only one possible signal model that allows for sampli ..."
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Cited by 110 (14 self)
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. We therefore concentrate on two aspects of the signal model, the existence of one to one maps to lower dimensional observation spaces and the smoothness of the inverse map. We show that almost all linear maps are one to one when the observation space is at least of the same dimension as the largest
On the finitedimensional PUA representations of the
, 1977
"... Abstract. The finitedimensional PUA representations of the Shubnikov space groups are discussed using the method of generalised induction given by Shaw and Lever. In particular we derive expressions for the calculation of the little groups. 1. ..."
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Abstract. The finitedimensional PUA representations of the Shubnikov space groups are discussed using the method of generalised induction given by Shaw and Lever. In particular we derive expressions for the calculation of the little groups. 1.
ON FINITEDIMENSIONAL MAPS
, 2002
"... Let f: X → Y be a perfect surjective map of metrizable spaces. It is shown that if Y is a Cspace (resp., dim Y ≤ n and dimf ≤ m), then the function space C(X,I ∞ ) (resp., C(X,I 2n+1+m)) equipped with the source limitation topology contains a dense Gδset H such that f ×g embeds X into Y ×I ∞ (res ..."
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Cited by 3 (1 self)
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Let f: X → Y be a perfect surjective map of metrizable spaces. It is shown that if Y is a Cspace (resp., dim Y ≤ n and dimf ≤ m), then the function space C(X,I ∞ ) (resp., C(X,I 2n+1+m)) equipped with the source limitation topology contains a dense Gδset H such that f ×g embeds X into Y ×I
Results 1  10
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1,570