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Jun 30, 2018
06/18

by
Alexander Borichev; Alon Nishry; Mikhail Sodin

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We study the influence of the multipliers $\xi (n)$ on the angular distribution of zeroes of the Taylor series \[ F_\xi (z) = \sum_{n\ge 0} \xi (n) \frac{z^n}{n!}\,. \] We show that the distribution of zeroes of $ F_\xi $ is governed by certain autocorrelations of the sequence $ \xi $. Using this guiding principle, we consider several examples of random and pseudo-random sequences $\xi$ and, in particular, answer some questions posed by Chen and Littlewood in 1967. As a by-product we show that...

Topics: Complex Variables, Probability, Mathematics

Source: http://arxiv.org/abs/1409.2736

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20

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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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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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

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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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Jun 30, 2018
06/18

by
Charles Batty; Alexander Borichev; Yuri Tomilov

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We prove $L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive $L^p$-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the $L^p$-rates of decay obtained in this way are best possible under our assumptions.

Topics: Complex Variables, Functional Analysis, Mathematics, Analysis of PDEs, Dynamical Systems

Source: http://arxiv.org/abs/1403.6084