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Sep 19, 2013
09/13

by
Alexander Borichev

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We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.

Source: http://arxiv.org/abs/math/0304199v1

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4.0

Jun 30, 2018
06/18

by
Alexander Borichev; Mikhail Sodin; Benjamin Weiss

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We will discuss a somewhat striking spectral property of finitely valued stationary processes on Z that says that if the spectral measure of the process has a gap then the process is periodic. We will give some extensions of this result and raise several related questions.

Topics: Classical Analysis and ODEs, Probability, Mathematics

Source: http://arxiv.org/abs/1701.03407

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63

Sep 22, 2013
09/13

by
Alexander Borichev; Don Hadwin; Hassan Yousefi

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We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are the finite-dimensional ones. We also characterize norm-stable invariant subspaces of any weighted unilateral shift operator. We show that quasianalytic shift operators are points of norm continuity of the lattice of the invariant subspaces. We also provide a...

Source: http://arxiv.org/abs/1001.1018v2

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43

Sep 23, 2013
09/13

by
Alexander Borichev; Prabhu Janakiraman; Alexander Volberg

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In this paper we address the question of finding the best $L^p$-norm constant for martingale transforms with one-sided orthogonality. We consider two martingales on a probability space with filtration $\mathcal{B}$ generated by a two-dimensional Brownian motion $B_t$. One is differentially subordinated to the other. Here we find the sharp estimate for subordinate martingales if the subordinated martingale is orthogonal and $1 2$, but the orthogonal martingale is a subordinator. The answers are...

Source: http://arxiv.org/abs/1012.0943v3