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91

Jul 20, 2013
07/13

by
Alexander Borichev; Omar El-Fallah; Abdelouahab Hanine

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We use the so called resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces.

Source: http://arxiv.org/abs/1304.0994v1

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19

Jun 28, 2018
06/18

by
Alexander Borichev; Andreas Hartmann; Karim Kellay; Xavier Massaneda

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We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities tend to infinity.

Topics: Mathematics, Complex Variables

Source: http://arxiv.org/abs/1508.03932

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19

Jun 28, 2018
06/18

by
Alexander Borichev; Andreas Hartmann; Karim Kellay; Xavier Massaneda

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We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities.

Topics: Mathematics, Complex Variables

Source: http://arxiv.org/abs/1508.03003

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59

Sep 20, 2013
09/13

by
Alexander Borichev; Prabhu Janakiraman; Alexander Volberg

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Burkholder obtained a sharp estimate of $\E|W|^p$ via $\E|Z|^p$, where $W$ is a martingale transform of $Z$, or, in other words, for martingales $W$ differentially subordinated to martingales $Z$. His result is that $\E|W|^p\le (p^*-1)^p\E|Z|^p$, where $p^* =\max (p, \frac{p}{p-1})$. What happens if the martingales have an extra property of being orthogonal martingales? This property is an analog (for martingales) of the Cauchy-Riemann equation for functions, and it naturally appears from a...

Source: http://arxiv.org/abs/1002.2314v3

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45

Sep 24, 2013
09/13

by
Yuri Bilu; Alexander Borichev

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We obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.

Source: http://arxiv.org/abs/1112.2290v2

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4.0

Jun 28, 2018
06/18

by
Anton Baranov; Yurii Belov; Alexander Borichev

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We describe the radial Fock type spaces which possess Riesz bases of normalized reproducing kernels and which are (are not) isomorphic to de Branges spaces in terms of the weight functions.

Topics: Functional Analysis, Complex Variables, Mathematics

Source: http://arxiv.org/abs/1512.09001

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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

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48

Sep 23, 2013
09/13

by
Alexander Borichev; Grigori Rozenblum

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We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The method of proving is different from the one used previously for finite rank theorems, and it enables one to get rid of the compact support condition for symbols imposed previously.

Source: http://arxiv.org/abs/1303.2996v1

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50

Sep 22, 2013
09/13

by
Alexander Borichev; Mikhail Sodin

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A long-standing open problem in harmonic analysis is: given a non-negative measure $\mu$ on $\mathbb R$, find the infimal width of frequencies needed to approximate any function in $L^2(\mu)$. We consider this problem in the "perturbative regime", and characterize asymptotic smallness of perturbations of measures which do not change that infimal width. Then we apply this result to show that there are no local restrictions on the structure of orthogonal spectral measures of...

Source: http://arxiv.org/abs/1004.1795v3

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14

Jun 28, 2018
06/18

by
Alexander Borichev; Artur Nicolau; Pascal J. Thomas

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Following Gorkin, Mortini, and Nikolski, we say that an inner function $I$ in $H^\infty$ of the unit disc has the WEP property if its modulus at a point $z$ is bounded from below by a function of the distance from $z$ to the zero set of $I$. This is equivalent to a number of properties, and we establish some consequences of this for $H^\infty/IH^\infty$. The bulk of the paper is devoted to "wepable" functions, i.e. those inner functions which can be made WEP after multiplication by a...

Topics: Functional Analysis, Mathematics, Complex Variables

Source: http://arxiv.org/abs/1508.01336