Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2017 Springer International Publishing AG

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Schema Evolution and Integration,n theorem” for such functions, comparing them with polynomials sharing their zeroes, and obtain an essentially sharp Remez-type inequality in the spirit of Yomdin (Isr J Math 186:45–60, 2011) for complex polynomials of one variable. Finally, based on these results, we present a Remez-type inequality for (., .)-valent functions.

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Commission

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发生

On Repeated Sequential Closures of Constructible Functions in Valuations,that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of the former space is equal to the latter one. This stronger property is necessary for some applications in Alesker (Geom Funct Anal 20(5):1073–1143, 2010).

integral

The Restricted Isometry Property of Subsampled Fourier Matrices,ix . obtained by randomly sampling . = .(. ⋅ log.. ⋅ log.) rows from an . × . Fourier matrix satisfies the restricted isometry property of order . with a fixed . with high probability. This improves on Rudelson and Vershynin (Comm Pure Appl Math, 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).

Isometric

Super-Gaussian Directions of Random Vectors,. We show that there exists a fixed unit vector . such that the random variable . satisfies . where . > 0 is any median of | . | , i.e., .. Here, . are universal constants. The dependence on the dimension . is optimal, up to universal constants, improving upon our previous work.

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