@unpublished{Tarkhanov2015,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A spectral theorem for deformation quantisation},
  volume    = {4},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425},
  pages     = {8},
  year      = {2015},
  abstract  = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.},
  language  = {en}
}
@unpublished{MeraShlapunovTarkhanov2015,
  author    = {Mera, Azal and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Navier-Stokes equations for elliptic complexes},
  volume    = {4},
  number    = {12},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85592},
  pages     = {27},
  year      = {2015},
  abstract  = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam{\´e} system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.},
  language  = {en}
}
@unpublished{MakhmudovMakhmudovTarkhanov2015,
  author    = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A nonstandard Cauchy problem for the heat equation},
  volume    = {4},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-83830},
  pages     = {14},
  year      = {2015},
  abstract  = {We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space with data on a strip lying on the lateral surface. The strip is of the form S x (0,T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S we derive an explicit formula for solutions of this problem.},
  language  = {en}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rad{\´o} theorem for p-harmonic functions},
  volume    = {4},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492},
  pages     = {10},
  year      = {2015},
  abstract  = {Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A.},
  language  = {en}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  volume    = {4},
  number    = {7},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78199},
  pages     = {11},
  year      = {2015},
  abstract  = {We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.},
  language  = {en}
}
@unpublished{GibaliShoikhetTarkhanov2015,
  author    = {Gibali, Aviv and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the convergence of continuous Newton method},
  volume    = {4},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-81537},
  pages     = {15},
  year      = {2015},
  abstract  = {In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.},
  language  = {en}
}
@unpublished{FedosovTarkhanov2015,
  author    = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich},
  title     = {Deformation quantisation and boundary value problems},
  volume    = {4},
  number    = {5},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150},
  pages     = {27},
  year      = {2015},
  abstract  = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.},
  language  = {en}
}
@unpublished{ElinShoikhetTarkhanov2015,
  author    = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic semigroups of holomorphic mappings and composition operators},
  volume    = {4},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914},
  pages     = {30},
  year      = {2015},
  abstract  = {In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.},
  language  = {en}
}
@unpublished{DereudreMazzonettoRoelly2015,
  author    = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie},
  title     = {An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers},
  volume    = {4},
  number    = {9},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80613},
  pages     = {23},
  year      = {2015},
  abstract  = {In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way.},
  language  = {en}
}
@unpublished{ConfortiRoelly2015,
  author    = {Conforti, Giovanni and Roelly, Sylvie},
  title     = {Reciprocal class of random walks on an Abelian group},
  volume    = {4},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604},
  pages     = {22},
  year      = {2015},
  abstract  = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.},
  language  = {en}
}
@unpublished{Conforti2015,
  author    = {Conforti, Giovanni},
  title     = {Reciprocal classes of continuous time Markov Chains},
  volume    = {4},
  number    = {8},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78234},
  pages     = {198},
  year      = {2015},
  abstract  = {In this work we study reciprocal classes of Markov walks on graphs. Given a continuous time reference Markov chain on a graph, its reciprocal class is the set of all probability measures which can be represented as a mixture of the bridges of the reference walks. We characterize reciprocal classes with two different approaches. With the first approach we found it as the set of solutions to duality formulae on path space, where the differential operators have the interpretation of the addition of infinitesimal random loops to the paths of the canonical process. With the second approach we look at short time asymptotics of bridges. Both approaches allow an explicit computation of reciprocal characteristics, which are divided into two families, the loop characteristics and the arc characteristics. They are those specific functionals of the generator of the reference chain which determine its reciprocal class. We look at the specific examples such as Cayley graphs, the hypercube and planar graphs. Finally we establish the first concentration of measure results for the bridges of a continuous time Markov chain based on the reciprocal characteristics.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2015,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weak boundary values of solutions of Lagrangian problems},
  volume    = {4},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617},
  pages     = {24},
  year      = {2015},
  abstract  = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.},
  language  = {en}
}