TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Root functions of elliptic boundary problems in domains with conic points of the boundary N2 - 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. T3 - Preprint - (2005) 07 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29812 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Operator algebras related to the Bochner-Martinelli Integral N2 - 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. T3 - Preprint - (2005) 04 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29789 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Harmonic integrals on domains with edges N2 - 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. T3 - Preprint - (2004) 20 KW - domains with singularities KW - de Rham complex KW - Neumann problem KW - Hodge theory Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26800 ER - TY - INPR A1 - Kytmanov, Aleksandr A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - Zeta-function of a nonlinear system N2 - Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn. T3 - Preprint - (2004) 19 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26795 ER - TY - INPR A1 - Kytmanov, Aleksandr A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - Power sums of roots of a nonlinear system N2 - For a system of meromorphic functions f = (f1, . . . , fn) in Cn, an explicit formula is given for evaluating negative power sums of the roots of the nonlinear system f(z) = 0. T3 - Preprint - (2004) 18 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26788 ER - TY - INPR A1 - Berman, Gennady A1 - Tarkhanov, Nikolai Nikolaevich T1 - Quantum dynamics in the Fermi-Pasta-Ulam problem N2 - We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability. T3 - Preprint - (2004) 05 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26695 ER - TY - INPR A1 - Gauthier, Paul M. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A covering property of the Riemann zeta-function N2 - For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails. T3 - Preprint - (2004) 03 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26683 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter N2 - Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation. T3 - Preprint - (2004) 02 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - On index theorem for symplectic orbifolds N2 - We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula. T3 - Preprint - (2003) 07 KW - star product KW - symmetry group KW - G-trace KW - G-index Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26550 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A fixed point formula in one complex variable N2 - 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. T3 - Preprint - (2003) 01 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26495 ER -