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  1. 3 Open Mathematics

Autorzy help

  1. 2 Ryazanov V.

  2. 1 Zaidenberg M.

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  1. 1 2016

  2. 1 2015

  3. 1 2009

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On the Riemann-Hilbert problem in multiply connected domains

100%
Ryazanov V.
Open Mathematics
|
2016
|
tom 14
|
nr 1
13-18
EN
We proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.
2
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Periodic harmonic functions on lattices and points count in positive characteristic

100%
Zaidenberg M.
Open Mathematics
|
2009
|
tom 7
|
nr 3
365-381
EN
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.
3
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Infinite dimension of solutions of the Dirichlet problem

88%
Ryazanov V.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
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