نتایج جستجو برای: isometry

تعداد نتایج: 2779  

Journal: :Bulletin of the London Mathematical Society 2017

Journal: :Annals of Pure and Applied Logic 2006

2007
M. Randall Ho M. R. Holmes

This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0, 1] of functions from [0, 1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0, 1]. It is shown that the closed linear span of an isometri...

Journal: :Linear Algebra and its Applications 2023

Let (S1,S2) be a bi-isometry, that is, pair of commuting isometries S1 and S2 on complex Hilbert space H. By the von Neumann-Wold decomposition, hyper-range H∞(S1):=∩n=0∞S1nH reduces to unitary operator. Although H∞(S1) is an invariant subspace for S2, in general, not reducing S2. We show isometry if only subspaces S2(ker⁡S1⁎) H are orthogonal. Further, we describe all bi-isometries satisfying ...

2011
Ming-Jun Lai Louis Y. Liu

We show that as long as the restricted isometry constant δ2k < 1/2, there exist a value q0 ∈ (0, 1] such that for any q < q0, each minimizer of the nonconvex `q minimization for the sparse solution of any underdetermined linear system is the sparse solution.

Journal: :CoRR 2012
Felix Krahmer Shahar Mendelson Holger Rauhut

We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sp...

Journal: :IEEE Trans. Information Theory 2009
T. Tony Cai Guangwu Xu Jun Zhang

This article considers constrained l1 minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise settings for two l1 minimization methods: the Dantzig selector and l1 minimization with an l2 constraint. The results of this paper improve the existing results in...

2009
Zhi Chen Yiqian Shi Bin Xu

Sixty years ago, S. B. Myers and N. E. Steenrod (Ann. of Math. 40 (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a stru ture of Lie group. Re ently A. V. Bagaev and N. I. Zhukova (Siberian Math. J. 48 (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we rstly show that the isometry group of a Riemannian manifold M wi...

Journal: :CoRR 2010
Holger Rauhut Justin K. Romberg Joel A. Tropp

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisitio...

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