Banach January 2010

banach@mathdept.okstate.edu

3 participants
12 discussions

Abstract of a paper by Shuheng Zhou
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "Restricted eigenvalue conditions on subgaussian random matrices" by Shuheng Zhou. Abstract: It is natural to ask: what kinds of matrices satisfy the Restricted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in $\R^p$, where $p$ is the dimensionality of the data, and show that a class of random matrices with independent rows, but not necessarily independent columns, satisfy the RE condition, when the sample size is above a certain lower bound. Here we explicitly introduce an additional covariance structure to the class of random matrices that we have known by now that satisfy the Restricted Isometry Property as defined in Candes and Tao 05 (and hence the RE condition), in order to compose a broader class of random matrices for which the RE condition holds. In this case, tools from geometric functional analysis in characterizing the intrinsic low-dimensional structures associated with the RE condition has been crucial in analyzing the sample complexity and understanding its statistical implications for high dimensional data. Archive classification: math.ST math.FA stat.ML stat.TH Remarks: 23 Pages The source file(s), graphs.tex: 71862 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.4045 or http://arXiv.org/abs/0912.4045 or by email in unzipped form by transmitting an empty message with subject line uget 0912.4045 or in gzipped form by using subject line get 0912.4045 to: math(a)arXiv.org.

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Abstract of a paper by Romain Demazeux
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "Weighted composition operators as Daugavet centers" by Romain Demazeux. Abstract: We investigate the norm identity $\|uC_\varphi + T\| = \|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$ is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy this equation for every weakly compact operator $T : C(S)\to C(S)$. We also give a characterization of such weighted composition operator acting on the disk algebra $A(D).$ Archive classification: math.FA Mathematics Subject Classification: 47B33, 47B38,46E15 Remarks: 18 pages The source file(s), Weighted_composition_operators_as_Daugavet_centers.tex: 57655 bytes, is(are) stored in gzipped form as 0912.4032.gz with size 15kb. The corresponding postcript file has gzipped size 112kb. Submitted from: romain.demazeux(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.4032 or http://arXiv.org/abs/0912.4032 or by email in unzipped form by transmitting an empty message with subject line uget 0912.4032 or in gzipped form by using subject line get 0912.4032 to: math(a)arXiv.org.

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Banach January 2010