TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types N2 - Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus T3 - Preprint - (2002) 06 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26255 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Anisotropic edge problems N2 - 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. T3 - Preprint - (2002) 09 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26280 ER - TY - INPR A1 - Witt, Ingo T1 - A calculus for a class of finitely degenerate pseudodifferential operators N2 - For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate. T3 - Preprint - (2002) 05 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26246 ER - TY - INPR A1 - Liu, Weian A1 - Yang, Yin A1 - Lu, Gang T1 - Viscosity solutions of fully nonlinear parabolic systems N2 - In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3]. T3 - Preprint - (2002) 02 KW - Viscosity solutions KW - systems of partial differential equations KW - fully non-linear degenerate parabolic equations KW - Perron's method KW - coupled solution Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26215 ER - TY - INPR A1 - Krainer, Thomas T1 - On the inverse of parabolic boundary value problems for large times N2 - We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consquences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is that the microlocal and global kernel structure of the inverse operator (solution operator) of a parabolic boundary value problem for large times is clarified. Moreover, our approach naturally yields qualitative pertubation results for the solvability theory of parabolic boundary value problems. To achieve these results, we assign t = ∞ the meaning of a conical point and treat the operators as totally characteristic pseudodifferential boundary value problems. T3 - Preprint - (2002) 12 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26310 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - Relative elliptic theory N2 - This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms. T3 - Preprint - (2002) 23 KW - Sobolev problem KW - elliptic morphism KW - (co)boundary operator KW - Green operator KW - index KW - Riemann-Roch theorem Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26400 ER - TY - INPR A1 - Davis, Simon T1 - On the absence of large-order divergences in superstring theory N2 - The genus-dependence of multi-loop superstring ams is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string pertubation theory, a result which is based only on the supersymmetric generalization of the polyakov measure and not the gauge group of the string model. T3 - Preprint - (2002) 28 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26452 ER - TY - INPR A1 - Schrohe, Elmar A1 - Seiler, Jörg T1 - The resolvent of closed extensions of cone differential operators N2 - We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0. T3 - Preprint - (2002) 19 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26378 ER - TY - INPR A1 - Kytmanov, Alexander A1 - Myslivets, Simona A1 - Tarkhanov, Nikolai Nikolaevich T1 - Holomorphic Lefschetz formula for manifolds with boundary N2 - The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary T3 - Preprint - (2002) 17 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26354 ER - TY - INPR A1 - Huicheng, Yin A1 - Witt, Ingo T1 - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data T3 - Preprint - (2002) 21 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26395 ER - TY - INPR A1 - Paneah, Boris T1 - Dynamic methods in the general theory of cauchy type functional equations N2 - Contents: 1 Introduction. Denfitions and Discussions 2 Solvability of the Cauchy Type Functional Equations 2.1 The Case of a P-configuration 2.2 The Case of a Z-configuration 2.3 Multiplicative Cauchy type functional equations 3 Problems in Analysis Reducing to Cauchy Type Functional Equations 3.1 Some problems in Integral Geometry and Cauchy Functional Equations 3.2 First Boundary Problem for Hyperbolic Differential Equations and Cauchy Type Functional Equations 4 Functional Equations Determining Polynomials T3 - Preprint - (2002) 10 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26295 ER - TY - INPR A1 - Krainer, Thomas T1 - On the calculus of pseudodifferential operators with an anisotropic analytic parameter N2 - We introduce the Volterra calculus of pseudodifferential operators with an anisotropic analytic parameter based on "twisted" operator-valued Volterra symbols. We establish the properties of the symbolic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side. In particular, we investigate the kernel cut-off operator via direct oscillatory integral techniques purely on symbolic level. We discuss the notion of parabolic for the calculus of Volterra operators, and construct Volterra parametrices for parabolic operators within the calculus. T3 - Preprint - (2002) 01 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26200 ER - TY - INPR A1 - Davis, Simon T1 - Connections and generalized gauge transformations N2 - The derivation of the standard model from a higher-dimensional action suggests a further study of the fibre bundle formulation of gauge theories to determine the variations in the choice of structure group that are allowed in this geometrical setting. The action of transformations on the projection of fibres to their submanifolds are characteristic of theories with fewer gauge vector bosons, and specific examples are given, which may have phenomenological relevance. The spinor space for the three generations of fermions in the standard model is described algebraically. T3 - Preprint - (2002) 29 KW - bundles KW - connections KW - fibre coordinates KW - parallelizable spheres KW - division algebras KW - force unification Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26468 ER - TY - INPR A1 - Davis, Simon T1 - On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer N2 - The Goldbach partitions of an even number greater than 2, given by the sums of two prime addends, form the non-empty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk. T3 - Preprint - (2002) 30 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26474 ER - TY - INPR A1 - Yin, Huicheng T1 - Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data N2 - In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point. T3 - Preprint - (2002) 07 KW - compressible Euler equations KW - lifespan KW - nondegenerate condition KW - shock wave Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26263 ER - TY - INPR A1 - Yin, Huicheng T1 - Global existence of a shock for the supersonic flow past a curved wedge N2 - This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally. T3 - Preprint - (2002) 08 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26272 ER - TY - INPR A1 - Witt, Ingo T1 - Local asymptotic types N2 - The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG-SIGAL's theory of the inversion of finitely meromorphic, operator-valued functions at a point. T3 - Preprint - (2002) 16 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26346 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Surgery and the relative index theorem for families of elliptic operators N2 - We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems. T3 - Preprint - (2002) 11 KW - elliptic operators KW - index theory KW - surgery KW - relative index KW - boundary value problems Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26300 ER - TY - INPR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Asymptotics and relative index on a cylinder with conical cross section N2 - We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula. T3 - Preprint - (2002) 27 KW - Meromorphic operator functions KW - relative index formulas KW - parameter-dependent cone operators Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26446 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators N2 - We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived. T3 - Preprint - (2002) 14 KW - elliptic family KW - conormal symbol KW - relative index KW - index formulas KW - symmetry conditions Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26327 ER -