@unpublished{ShlapunovTarkhanov2012,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57759},
  year      = {2012},
  abstract  = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.},
  language  = {en}
}
@unpublished{Siegert2010,
  author    = {Siegert, Sabine},
  title     = {Das Sankt-Petersburg-Paradoxon},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49595},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1 Einleitung 2 Historische L{\"o}sungsans{\"a}tze 3 Martingal-Ansatz 4 Markovketten-Ansatz 5 Asymptotische Interpretationen 6 Bezug zur Praxis 7 R{\´e}sum{\´e} Anhang Literaturverzeichnis},
  language  = {de}
}
@unpublished{SultanovKalyakinTarkhanov2014,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@unpublished{Tarkhanov2015,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{Tarkhanov2002,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Anisotropic edge problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26280},
  year      = {2002},
  abstract  = {We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.},
  language  = {en}
}
@unpublished{Tarkhanov2004,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Harmonic integrals on domains with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26800},
  year      = {2004},
  abstract  = {We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.},
  language  = {en}
}
@unpublished{Tarkhanov2006,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Euler characteristic of Fredholm quasicomplexes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30117},
  year      = {2006},
  abstract  = {By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes. The paper is to appear in Funct. Anal. and its Appl., 2006.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Root functions of elliptic boundary problems in domains with conic points of the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29812},
  year      = {2005},
  abstract  = {We prove the completeness of the system of eigen and associated functions (i.e., root functions) of an elliptic boundary value problem in a domain whose boundary is a smooth surface away from a finite number of points, each of them possesses a neighbourhood where the boundary is a conical surface.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Operator algebras related to the Bochner-Martinelli Integral},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29789},
  year      = {2005},
  abstract  = {We describe a general method of computing the square of the singular integral of Bochner-Martinelli. Any explicit formula for the square applies in a familiar way to describe the C*-algebra generated by this integral.},
  language  = {en}
}
@unpublished{Tarkhanov2012,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A simple numerical approach to the Riemann hypothesis},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57645},
  year      = {2012},
  abstract  = {The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {On the root functions of general elliptic boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29822},
  year      = {2005},
  abstract  = {We consider a boundary value problem for an elliptic differential operator of order 2m in a domain D ⊂ n. The boundary of D is smooth outside a finite number of conical points, and the Lopatinskii condition is fulfilled on the smooth part of δD. The corresponding spaces are weighted Sobolev spaces H(up s,Υ)(D), and this allows one to define ellipticity of weight Υ for the problem. The resolvent of the problem is assumed to possess rays of minimal growth. The main result says that if there are rays of minimal growth with angles between neighbouring rays not exceeding π(Υ + 2m)/n, then the root functions of the problem are complete in L²(D). In the case of second order elliptic equations the results remain true for all domains with Lipschitz boundary.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Unitary solutions of partial differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29852},
  year      = {2005},
  abstract  = {We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.},
  language  = {en}
}
@unpublished{Tarkhanov2003,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A fixed point formula in one complex variable},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26495},
  year      = {2003},
  abstract  = {We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.},
  language  = {en}
}
@unpublished{TarkhanovVasilevski2005,
  author    = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai},
  title     = {Microlocal analysis of the Bochner-Martinelli integral},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30012},
  year      = {2005},
  abstract  = {In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szeg{\"o} projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.},
  language  = {en}
}
@unpublished{TarkhanovWallenta2012,
  author    = {Tarkhanov, Nikolai Nikolaevich and Wallenta, Daniel},
  title     = {The Lefschetz number of sequences of trace class curvature},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56969},
  year      = {2012},
  abstract  = {For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.},
  language  = {en}
}
@unpublished{Tepoyan2000,
  author    = {Tepoyan, Liparit},
  title     = {Degenerated operator equations of higher order},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25888},
  year      = {2000},
  abstract  = {Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation},
  language  = {en}
}
@unpublished{Tepoyan2008,
  author    = {Tepoyan, Liparit},
  title     = {The mixed problem for a degenerate operator equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30334},
  year      = {2008},
  abstract  = {We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.},
  language  = {en}
}
@unpublished{VasilievTarkhanov2016,
  author    = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich},
  title     = {Construction of series of perfect lattices by layer superposition},
  volume    = {5},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591},
  pages     = {11},
  year      = {2016},
  abstract  = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.},
  language  = {en}
}
@unpublished{Voss2010,
  author    = {Voss, Carola Regine},
  title     = {Harness-Prozesse},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49651},
  year      = {2010},
  abstract  = {Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgef{\"u}hrt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen {\"u}ber Z beziehungsweise R+ nachzuweisen.},
  language  = {de}
}
@unpublished{Wallenta2013,
  author    = {Wallenta, Daniel},
  title     = {A Lefschetz fixed point formula for elliptic quasicomplexes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016},
  year      = {2013},
  abstract  = {In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.},
  language  = {en}
}