@unpublished{FedchenkoTarkhanov2014,
author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
title = {An index formula for Toeplitz operators},
volume = {3},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499},
pages = {24},
year = {2014},
abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.},
language = {en}
}
@unpublished{MakhmudovTarkhanov2014,
author = {Makhmudov, Olimdjan and Tarkhanov, Nikolai Nikolaevich},
title = {The first mixed problem for the nonstationary Lam{\´e} system},
volume = {3},
number = {10},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943 (online)},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71923},
pages = {19},
year = {2014},
abstract = {We find an adequate interpretation of the Lam{\´e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam{\´e} system.},
language = {en}
}
@unpublished{SultanovKalyakinTarkhanov2014,
author = {Sultanov, Oskar and Kalyakin, Leonid and Tarkhanov, Nikolai Nikolaevich},
title = {Elliptic perturbations of dynamical systems with a proper node},
volume = {3},
number = {4},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70460},
pages = {12},
year = {2014},
abstract = {The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.},
language = {en}
}
@unpublished{AizenbergTarkhanov2014,
author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
title = {An integral formula for the number of lattice points in a domain},
volume = {3},
number = {3},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70453},
pages = {7},
year = {2014},
abstract = {Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.},
language = {en}
}
@unpublished{DyachenkoTarkhanov2014,
author = {Dyachenko, Evgueniya and Tarkhanov, Nikolai Nikolaevich},
title = {Singular perturbations of elliptic operators},
volume = {3},
number = {1},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69502},
pages = {21},
year = {2014},
abstract = {We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.},
language = {en}
}