bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparison Properties of the Cuntz
Semigroup and Applications to C* -algebras
Authors: Bosa Joan , Petzka Henning
Published: December 2016

We study comparison properties in the category Cu aiming to lift results to the C* -algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property (CFP) and ω-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for C* -algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear C* -algebra with a finite and an inifnite projection does not have the CFP.
Über Grundlösungen von Differenzenoperatoren
Authors: Pfeifer Eckehard , Rauhöft Angela
Published: December 2016

The method to solve problems of the mathematical physics using the so-called fundamental solutions and its properties is well-known. There is the question how does it work in the case of finite difference equations approximating the mentioned problems. An answer can be given treating difference equations as functional equations in certain spaces of distributions. By a suitable construction it is shown that every linear forward difference operator with constant coefficients possesses a tempered fundamental solution in a neighbourhood (with respect to the discretisation parameter) of the fundamental solution of the corresponding differential operator. An initial-value problem for the one-dimensional equation of heat conduction as an example for a useful application of discrete fundamental solutions closes the paper.
Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume
Authors: Kürsten Klaus-Detlef
Published: December 2016

Let

(E_i)_U

be the ultraproduct of ordered Banach spaces and let

L

be a finite dimensional sub-space of the dual

(E_i)_u^*

. Then there exists a positive iscmetric imbedding of

L

into

(E_i^*)_U

also satisfying some additional conditions In the case of Banach lattices the isometric imbedding may be chosen as a lattice homomorphism. Similar but somewhat weaker positivity properties can be satisfied for the almost isometric imbeddings of finite dimensional subspaces of

E^{**}

into

E

which exist by the principle of local reflexivity.
Interior Estimates for Singularly Perturbed Problems
Authors: Göhde Dietrich
Published: December 2016

The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation

\epsilon L_1u + L_0u = h

of order

2m

converges, for

\epsilon \to 0

, outside of the boundary layer uniformly to a solution of the degenerate elliptic equation

L_0w = h

of lower order. It is shown in the case of order zero of

L_0

this assertion may be proved immediately, i.e., without the usual construction of boundary layer terms, but rather elementary and on weak smoothness conditions with respect to the boundary of the domain.
Nonlocal Nonlinear Problems for One-Dimensional Parabolic System
Authors: Chrzanowski Eugeniusz M.
Published: December 2016

In the paper two nonlocal, nonlinear problems for a system of parabolic equations are considered:

to find a solution of the system

\vec u_t (x,t) = D\vec u_{xx}(x, t) + \vec f (x, t, \vec u (x, t))

subject to the conditions

\vec u (0, t) = \vec \varphi (t), \quad t \in (0, T),

\vec u (x, 0) = \vec \psi (x), \quad x \in (0, 1),

\vec u (1, t) - \vec u (x_0, t) = \vec h (x_0, t, \vec u (x_0, t))

or

\int ^1_0 \vec u (x, t) dx = \vec g (t).

For this an operator

L: C(\bar \Omega) \to C(\bar \Omega)

being a sum of four potentials is constructed. It is shown that the operator

L

has only one fixed point. Moreover it is proved that the fixed point is the only solution of the considered problem.
Infinite Representability of Schrödinger Operators with Ergodic Potential
Authors: Englisch Harald , Kürsten Klaus-Detlef
Published: December 2016

Analogous to the notion of finite representability in the theory of Banach spaces, the notions of the representability and the infinite representability of self-adjoint operators are introduced. It is proved that the infinite representability of the operator

A

in

B

yields that the essential spectrum of

B

contains the spectrum of

A

. This result applied to ergodic Schrödinger operators yields a new proof for the nonrandomness of the spectrum and for the connection between the spectrum and the density of states. A formula for the spectrum of the Hamiltonian of a substitutional alloy is presented, which clarifies the bowing effect. Similar results were found independcntly by Kirsch and Martinelli.
On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from Stochastics
Authors: Doppel Karl , Jacob Niels
Published: December 2016

Recently E. B. Dynkin [2] introduced and studied a non-hypoelliptic linear partial differential operator of even order (with constant coefficients) which originates from the theory of multi-parametric stochastic processes. Motivated by the consideiations of Dynkin the authors have solved a generalized Dirichlet problem for this differential operator in their work [1]. Our aim in the present paper is to investigate the Cauchy problem for the corresponding evolution equation (in the time variable of first order); such a Cauchy problem could have applications to some questions from the stochastics.
Zur numerischen Bestimmung des Abbildungsgrades im $\mathbb R^n$ II
Authors: Kliesch Wolfgang
Published: December 2016

In this part of the paper, special formulas are deduced from the representations of the topological degree introduced in the first part. Partially, these formulas are generalizations of well-known formulas. Thus, possible means are given for unified approach to the computational formulas for the topological degree used in numerical analysis. Further it is shown how, using Kuhnsimplices, the topological degree can be used for existence proofs and error estimations for zeros of nonlinear equations. Results of some computational tests are given in the last section.
Zur Unität der Lösung der Theodorsenschen Integralgleichung der konformen Abbildung
Authors: von Wolfersdorf Lothar
Published: December 2016

In the paper a new proof of the uniqueness of the continuous solution to the Theodorsen integral equation of conformal mapping is given.
Extremalprinzipien zur Charakterisierung von quasikonformen Normalabbildungen und ihre Anwendung zur Abschätzung von Gebietsfunktionalen
Authors: Kirsch Siegfried
Published: December 2016

For a certain class of quasiconformal canonical mappings of a multiple-connected domain the extremal principle is derived with the help of the energy-principle of the modern potential theory, and several distorsion theorems and estimations of domain functionals are proved.
Remarks on Duality Mapping and the Lax-Milgram Property
Authors: Kolomý Josef
Published: December 2016

Some conditions under which the duality map is a homeomorphism from a Banach space

X

onto

X \ast

and upper-semicontinuous at some dense subset of

X

are derived. Some further pro-perties of the duality mapping are established in connection with the structure of the Banach space

X

. The so-called Lax-Milgram property of the bilinear forms is also investigated.
Coefficient Control in a Linear Second Order Ordinary Differential Equation
Authors: Goebel Manfred , Begashaw Negash
Published: December 2016

In this paper we deal with a control problem whose behaviour is described by the solution of a linear boundary value problem of a second order ordinary differential equation. The coefficient of the first derivative in the state equation is assumed to be the control. We prove the existence of optimal control and discuss its uniqueness. Moreover, we formulate both necessary and sufficient optimality conditions.
Eine Verallgemeinerung des Ritz-Prozesses
Authors: Hofmann Reinhard
Published: December 2016

An approximative process for the projection of an element of a Hilbert space on a finite-dimensional subspace is proposed where the subspace is given only in an implicit manner. Both the convergence and numerical measures of convergence are studied and any conditions are given for the process to be stable in the sens of Michlin. As an application we point out the problem to minimize the middle strain in a plate where are varied the boundary powers only.
A Remark on a Paper by D. E. Edmunds, A. Kufner and J. Râkosnfk
Authors: Triebel Hans
Published: December 2016

The paper deals with approximation properties in weighted spaces of Sobolev-Slobodeckij type.
Twistprodukt und Quasi-*-AIgebren
Authors: Lassner Gerd , Lassner Gisela A.
Published: December 2016

The Schwartz distribution space

\mathcal S’

becomes a topological quasi-*-algebra with the distinguished subspace

\mathcal S

, if one defines the so-called twisted product in it. In the paper it is pointed out that the Weyl quantization

f \to W(f)

IV(/) is an isomorphism of this topological quasi-*-algebra onto the topological quasi-*-algebra

\mathcal L (\mathcal S, \mathcal S’)

of all linear continuous operators of

\mathcal S

in

\mathcal S’

. Furthermore, the problem of the extensions of the multiplications in these quasi-*-algebras is discussed.
Bifurcation and Stability of Cellular States in Magnetic Fluids
Authors: Beyer Klaus
Published: December 2016

This paper continues earlier work by the author concerning bifurcation and stability of periodic equilibrium states of a magnetic fluid subjected to a vertical magnetic field. Here the treatment is extended to cover the case of a fluid of finite depth.
Über einen Vergleichssatz
Authors: Morgenthal Klaus
Published: December 2016

A comparison theorem for the functional-differential inequalities

x’(t) \leq \geq l(t) x(t) - \int^{\sigma(t)}_{\tau = 0} x(t - \tau) dr(t, \tau)\quad \quad (- \infty < A ≤ t < B ≤ + \infty)

is proved wich generalizes results of E. Kozakiewicz and A. D. Myskis.
Ein Regularitätssatz für ein lineares System von Variationsungleichungen mit einer Halbraumnebenbedingung
Authors: Fuchs Martin
Published: December 2016

We consider linear non-diagonal elliptic systems of variational inequalities where the admissible class of functions is characterized by Dirichlet boundary conditions and a half-space constraint

u \cdot a \geq \theta

for some fixed vector

a \in \mathbb R^n

. By potential theoretic arguments we show continuity of the solution provided the obstacle

\theta \colon \Omega \to \mathbb R

is a continuous function.
An Existence Theorem for a Quasilinear Hyperbolic Boundary Value Problem Solved by Semidiscretization in Time
Authors: Pluschke Volker
Published: December 2016

By the use of Rothe’s method there is proved the existence of a solution of a quasilinear hyperbolic boundary value problem. On the coefficients and the right-hand side only integrability is assumed. With such weak assumptions there exists a subsequence of Rothe approximations that converges (in a weak sense) to a solution of the problem.
Non-Negative Trigonometric Polynomials with Constraints
Authors: Ruscheweyh Stephan
Published: December 2016

We discuss extremal problems for non-negative trigonometric polynomials with prescribed zeros. The general result is used to refine a former theorem of Fejér concerning upper bounds of those polynomials near to a zero. Another application deals with the coefficient problem for typically real (algebraic) polynomials.
Entartete lineare elliptische Differentialgleichungen und anisotrope Sobolewräume: Existenz schwacher Lösungen
Authors: Herrler Hans-Jürgen
Published: December 2016

This paper deals with Dirichiet boundary value problems for degenerated linear elliptic systems in bounded domains. Generalising the condition of strong ellipticity we extend the theory of weak solutions to a class of certain systems. In these ones the highest derivatives with respect to several variables or to several unknowns have different orders. For such system Gårding’s inequality in anisotropic Sobolov spaces can be proved. In this way we get existence and uniqueness results for weak solutions.
Ein System stationärer partieller Differentialgleichungen des Ladungsträgertransportes in Halbleitern
Authors: Kluge Reinhard , Unger Steffen
Published: December 2016

Different boundary value problems for the system of stationary partial differential equations for the carrier transport in semiconductors are considered in corresponding subspaces of the product

W_r^1(G) \times W_p^1(G) \times W_p^1(G)

with Sobolev-spaces

W_q^1(G), q = r

and

q = p

. The domain

G \subset \mathbb R^n (n = 1,2,3)

is supposed to be bounded and

p

and

r

are in general different. The paper contains the proof of the existence of solutions in the whole scale

2n/(n + 1) < p < + \infty

with corresponding restrictions for

r > 1

, estimations from above for the diameter of the solution set and some uniqueness results.
Maximal Monotone Operators and Saddle Functions I
Authors: Krauss Eckehard
Published: December 2016

We investigate the monotone operator

T_K \subseteq E \times E^*, f \in T_Kx\colon = [–f, f] \in \partial K(x,x)

, which is defined via the subdifferential of a concave-convex saddle function

K

. Our considerations are motivated by the fact that each maximal monotone operator

A

possesses a representation of the form

A = T_K

. We show that

T_K

is maximal monotone if and only if

K

is in a relaxed form skew-symmetric. This allows a generalization of results obtained previously.
Über ebene Bimetallprobleme für das Aussengebiet mit verschiedenen Rand- und Kontaktbedingungen
Authors: Jentsch Lothar
Published: December 2016

Existence and uniqueness theorems for boundary contact problems of plane elastostatics for the exterior domain are proved for the case whenithe boundary and the contact-line have common points. Two boundary and three different contact conditions are considered. The differential equation and the contact condition are a priori fulfilled by potentials having the corresponding contact tensor as kernel. The densities of the potentials satisfy systems of integral equations with fixed singularities, the Fredholm property of which follows from results of Duduchava.
Uniqueness Theorems for the Determination of a Coefficient in a Quasilinear Parabolic Equation
Authors: Dümmel Siegfried
Published: December 2016

Two uniqueness theorems for the determination of the coefficient

q(u)

in the quasilinear parabolic equation

u_t = q(u) \Delta u

are proved for the case that

q

is analytic and for the special case that

q

depends linearly on

u

.
Ein transfiniter Durchmesser bei quasikonformen Normalabbildungen mehrfach zusammenhängender Gebiete
Authors: Kirsch Siegfried
Published: December 2016

The transfinite diameter of Fekete of a simply connected domain, which is connected with the conformal radius of the domain, is generalized for a certain class of quasiconformal canonical mappings of a multiply connected domain. For the conformal case the rate of convergence is studied.
The Green Matrix for Strongly Elliptic Systems of Second Order with Continuous Coefficients
Authors: Fuchs Martin
Published: December 2016

We study a generalization of the Green function for elliptic equations to elliptic systems of second order with continuous coefficients. The existence and uniqueness of such a Green matrix as well as various estimates concerning the growth properties near the singular diagonal are proved. Moreover, one can derive representation formulas for solutions of elliptic systems and deduce from these further information about the solution even in the case when the right-hand side of the system is a vector-valued measure of bounded variation.
Extremalprobleme quasikonformer Abbildungen der Ebene als Steuerungsprobleme
Authors: Dittmar Bodo
Published: December 2016

A new method for solving extremal problems of quasiconformal mappings is presented. The extremal problem is interpreted as a control problem. Necessary conditions are proved and analysed.
Nichtlineare Evolutionsgleichungen für $q$-holomorphe Vektoren
Authors: Crodel Andreas
Published: December 2016

Initial value problems for evolution processes are considered in spaces of

q

-holomorphic vectors and theorems of the Cauchy–Kovalevskaja type are proved for these problems.
On the Optimality of Methods for Ill-Posed Problems
Authors: Vainikko Gennadi
Published: December 2016

The optimality of a class of regularization methods for linear ill-posed problems is investigated. The general results are applied to Lavrentjew’s and Tikhonov’s methods and to a class of iteration methods and their continuous versions.
Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssytemen in statischen Raum-Zeiten
Authors: Illge Reinhard
Published: December 2016

The already known necessary conditions for the validity of Huygens’ principle for the self-adjoint scalar wave equation, for Maxwell’s and Weyl’s equations are examined in static space-times by the help of the spinor calculus. One result is, that Huygens’ principle does not hold in Riemannian spaces, whose metric tensor is static and whose Weyl spinor is of Petrov type D. If two of the three considered types of equations satisfy Huygens’ principle in a static space-time, then the conformal curvature tensor vanishes.
Second Microlocalization and Propagation Theorems for the Wave Front Sets
Authors: Esser Patrick
Published: December 2016

There is showed how to define the second analytic wave front set in order to obtain propagation properties for differentiable, Gevrey, or analytic singularities of distributions without second analytic support.
On Commutators in Algebras of Unbounded Operators
Authors: Timmermann Werner
Published: December 2016

For diagonal, quasidiagonal and finite dimensional operators in topological algebras of unbounded operators there are given several criteria which imply their representation as I commutators. It is proved that the commutators are dense in the maximal Op*-algebra with respect to the uniform topology. Simple facts about selfcommutators, some conjectures and problems are given.
An Explicit Expression for the Korteweg–de Vries Hierarchy
Authors: Schimming Rainer
Published: December 2016

An explicit representation for the Korteweg–de Vries hierarchy of solitonic partial differential equations is derived which has not been known before.
Modular Interpolation Spaces I
Authors: Krbec Miroslav
Published: December 2016

An interpolation method in modular spaces is introduced and basic properties of obtained interpolation spaces are studied (completness, imbeddings etc.). The main result hero is a reiteration theorem. It is shown how the method works in Orlicz spaces and as an example of applications there is proved a multiplier theorem of the Michlin type. The method generalizes the

K

-method of Peetre.
Regulare Aufgaben der optimalen Steuerung mit linearen Zustandsrestriktionen
Authors: Phú Hoàng Xuân
Published: December 2016

A class of regular optimal control problems with linear state restrictions is investigated by the author’s method of region analysis. This method may find out the behaviour of the optimal state function with respect to the state restrictions and, in favourable cases, even the optimal solution. For example, a geometrical optimization problem is solved.
A Lattice Problem for Differential Forms in Euclidean Spaces
Authors: Schuster Reinhard
Published: December 2016

Generalizing a lattice-point problem we solve a lattice problem for

\mathfrak G

-automorphic differential

p

-forms in the

n

-dimensional Euclidean space

\mathbf E^n

, where

\mathfrak G

is a properly discontinuous group of isometrics of

\mathbf E^n

with compact fundamental domain. Our approach essentially uses mean value operators for differential forms and a Landau difference method.
On the Nonlinear Boltzmann Equation of the Carrier Transport in Semiconductors II: Numerical Approximation of Solutions
Authors: Hanke Michael
Published: December 2016

A collocation method for the numerical solution of a special kind of the steady-state nonlinear Boltzmann equation used in the transport theory in semiconductors is proposed and the convergence of the method is proved.
Interpretation of Variations of the Earth’s Vector of Rotation Using Inverse Solution
Authors: Jochmann Horst
Published: December 2016

Global geophysical processes cause variations of the Earth’s vector of rotation. If only little information on these processes is available, it is suitable to consider the solution of the Euler-Liouville equations as an inverse problem. A global oscillation of the sea level (with a 4–5 years period) between the north and the south hemisphere of the Earth could be proved in this way for the first time.
On the Identification of the Adiabatic Equation of State in Compressible Gas Flow
Authors: Kleine Eckhard
Published: December 2016

The inverse problem of determining the coefficient in the differential equation

\bigtriangledown (\varrho \bigtriangledown \varphi) = 0, \varrho = \varrho (| \bigtriangledown \varphi |)

is considered. The underlying idea is demonstrated by a consideration of gas dynamics. An appropriate formulation of the problem yields an explicit solution.
On Parameter Identification for Ordinary Differential Equations
Authors: Tautenhahn Ulrich
Published: December 2016

The regularized solution of identification problems in ordinary differential equations is investigated when the data are noisy. For minimizing the occurring regularization functionals the gradient method and the Gauss-Newton method are examined by exploiting the concept of adjoint equations. An application to a particular inverse problem arising in the study of water movement about a gas-storage reservoir of aquifer type completes the paper.
Basic Properties of Some Differential-Algebraic Equations
Authors: Griepentrog E. , März Roswitha
Published: December 2016

The solvability of the equation

Ax’ + Bx = q

with a regular modified local matrix pencil of higher index is considered. It is shown how to formulate initial conditions properly and that the initial value problems lead to operators with unbounded inverses. The close relationship of the matrix pencils needed in the investigation and of the related chains of the reduction methods is pointed out.
The Galerkin method for parabolic equations with operators of local type (in Russian)
Authors: Oja Peeter
Published: December 2016

The existence and the uniqueness of solution are investigated for the Cauchy problem

u’(t) + A(t) u(t) + (Mu) (t) = f(t), u(0) = u_0

, with a family of linear operators

A(t)

and a local typo operator

M

. In the applications

M

represents, in particular, the retardation of the argument or an integral operator. It is shown that this Cauchy problem produces an isomorphism between some natural spaces of given data and solutions. The convergence of the Galerkin method takes place in strong norms containing derivatives by t. The rate of convergence is characterized by two-sided estimates. The influence of perturbations, arising in the course of calculating the coefficients of the approximate problem as scalar products, on the approximate solutions is given also by two-sided estimates in the same norms in which the convergence is proved.
Bernstein-Sato-Polynome und Faltungsgruppen zu Differentialoperatoren
Authors: Wagner Peter
Published: December 2016

This work relies on Bernstein’s method of analytic continuation of the distribution-valued function

P^1

(

P

a polynomial) with respect to the complex exponent 2. In the case of a homogeneous, elliptic partial differential operator

P(\mathrm i \partial / 2 \pi)

, the convolvability and the validity of the relation

T_{\lambda} \cdot T_{\mu} = T_{\lambda + \mu}

in the “convolution group”

\{T_{\lambda}\}

, which corresponds to

P^1

through Fourier transform, is characterized by a condition on the indices

\lambda, \mu

. In this way, we generalize the known convolution properties of the elliptic Riesz kernels

R_{\lambda}

, which represent the convolution group of the Laplacean operator. In a second part, Bernstein’s process of analytic continuation is carried out in a constructive manner in the special case of the polynomial

P

being of the form

x_1^m + \cdots + {x'}_n^m

. The importance of this process for the computation of fundamental solutions of the powers of the corresponding differential operator

P(\mathrm i \partial / 2 \pi)

is illustrated in working out the example

\partial _1^4 + \partial _2^4

.
Analytic Realization of Relative K-Homology on Manifolds with Boundary and Pairing with K-Cohomology
Authors: Douglas Ronald G. , Wojciechowski Krysztof P.
Published: December 2016

Although K-homology can be defined abstractly as a dual of the ordinary K-theory of spaces, its use in index theory and analysis comes about through the concrete realization where elliptic operators are cycles. This is well understood for manifolds without boundary but not when a boundary is present. In this note we provide a realization for relative cycles using elliptic operators on the doubled manifold and explore pairings of these cycles with K-cohomology in terms of Fredholm indexes and spectral flow.
Solution in Quadratures of the Basic Problems of Thermoelasticity for a Sphere and a Spherical Cavity
Authors: Chichinadze Rafiel K. , Gegelia Tengiz G.
Published: December 2016

The basic static problems of classical thermoelasticity are solved in quadratures for a sphere and the entire space with a spherical cavity. The solution is constructed under the most general and natural restrictions. Many boundary value problems of mathematical physics are reduced by means of special potentials to singular integral equations. For some domains these equations are solved explicitly and solutions of the corresponding boundary value problems are constructed in quadratures. For domains with a spherical boundary it appears to be convenient to use a special representation of solutions sometimes called the Trefftz representation (see, for example, [9] or [16]) but evidently occuring for the first time as early as 1904 in a paper of Marcolongo [11]. It is shown that this representation is also valid for problems of thermoelasticity.
Zur Regularisierung des Systems, bestehend aus den Reynolds-Gleichungen und dem $k-\varepsilon$-Modell der Turbulenz
Authors: Kluge Reinhard
Published: December 2016

We consider a system of nonlinear partial differential equations consisting of the Reynolds equations and of the

k-\varepsilon

model of turbulence in the three-dimensional stationary case for the heat and mass transfer in incompressible viscous flows. For regularizations of this system we prove the existence of weak solutions. In this connection we use a new existence result for nonlinear variational inequalities.
A Nehari Type ProbIem for Matricial Schur Functions
Authors: Fritzsche B. , Kirstein B.
Published: December 2016

Using Schur analysis methods a particular completion problem for matricial Schur functions will be treated which can be conceived as an analogue of a generalized Nehari problem for matricial Carathéodory functions recently studied by the authors.
Konvergenzbeschleunigung bei Potenzreihen durch asymptotische Entwicklung der Restsummen
Authors: Riedel Roland
Published: December 2016

Asymptotic expansions for the residual sums of power series are derived by the asymptotical behavior of the coefficients. Finite parts at these expansions areu sed for the acceleration of convergence.
An Existence Theorem for General Control Problems of Nonlinear Evolution Equations of First Order
Authors: Krause Bernd
Published: December 2016

An existence theorem for the solution of optimal control problems of systems governed by the state equation

y+ vAy + B(y) = u

is proved, where

A

is a linear operator and

B

a nonlinear operator with

||B(y)||_n ≤ c(1 + ||y||_m^r)

.
On the Existence of Conjugate Points for Sturm–Liouville Differential Equations
Authors: Müller-Pfeiffer Erich , Schott Th.
Published: December 2016

By means of integral conditions for the coefficients

p

and

q

of Sturm-Liouville differential equations

—(p(x) u’)’ + q(x) u = 0

the distance between consecutive zeros of non-trivial solutions

u

will be estimated from above.
A regularization method in the Cauchy problem for holomorphic functions
Authors: Wagner Eberhard , von Wolfersdorf Lothar
Published: December 2016

In the paper a regularization method in the Cauchy problem for holomorphic functions in the unit disk is proposed, which relies on the embedding of this problem into a family of Carleman conjugacy problems.
Self-Duality and $C*$-Reflexivity of Hilbert $C*$-Moduli
Authors: Frank Michael
Published: December 2016

The subjects of this paper are a new definition of the notion "self-dual Hilbert

C*

-module" as a- categorical concept of Banach

C*

-moduli, and the conditions for some Hilbert

C*-moduli to be self-dual or

C*

-reflexive. The isomorphism of any two Hilbert structures on a given self-dual Hilbert

C*

-module inducing equivalent norms to the given one is stated. A topological criterion of self-duality and

C*

reflexivity of Hilbert

W*

-moduIi is proved. A criterion of self-duality of the countably generated Hilbert

\mathcal A

-module

l_2(\mathcal A)

is stated for arbitrary

C*

-algebras

\mathcal A$. As an application the classification of countably generated Hilbert W*modimli by their structure is given.
A Characterization of Pobrushin’s Coefficient of Ergodicity
Authors: Kühne Rolf , Rhodius Adolf
Published: December 2016

It is proved that the ergodicity coefficient

\tau

corresponding to any vector norm on

\mathbb R^n

fulfills the inequality

\tau (P) ≤ 1

for all

n \times n

stochastic matrices

P

if it is the Dobrushin ergodicity coefficient.
Approximation durch Lösungen elliptischer Randwertprobleme auf nichtglatten Gebietsrändern
Authors: Hamann Uwe
Published: December 2016

Let

\Omega \subset \mathbb R^n

be a bounded, smootI domain and

\Gamma

the (not necessary smooth) boundary of an open set

\Omega_i \subset \subset \Omega

. it is investigated, under which conditions given tuples of continuous functions (Whitney-Taylorfields) on

\Gamma

can be uniformly approximated by solutions of elliptic boundary value problems with respect to

\Omega

.
Factoring Compact Operators and Approximable Operators
Authors: Popovici Ioan Mircea , Vuza Dan Tudor
Published: December 2016

Our paper is concerned with two topics. The first one is represented by aversion of Figiel’s and Johnson’s theorem on the factorization of compact operators adapted to the framework of ordered Banach spaces. Namely, we prove that every compact operator from a Banach space to an ordered Banach space with closed generating cone (respectively, a Banaöh lattice) factors, with compact factors, through a reflexive lattice-ordered Banach space with closed generating cone, the second factor being positive (respectively, a reflexive lattice-ordered Banach space with continuous modulus, the second factcr being a Riesz homomorphism).

The second topic is provided by a discussion of the factorization of approximable operators between :Banach lattices. We prove that every such operator

U

factors through a reflexive Banach lattice with an unconditional basis, the factors being compact and one of them being positive. We also give a necessary and sufficient condition on

U

under which both factors in the mentioned factorization can be taken to be differences of positive compact operators.
On Uniform Limitability and Banach Limits
Authors: Schatte Peter
Published: December 2016

A bounded sequence is shown to be

H_{nifty}

-limitable to the value

a

if and only if all strong Banach limits assign the same value a to this sequence. In this connection, a strong Banach limit means a linear functional with certain properties on the space

M

of bounded sequences. More general uniform limitation methods can be characterized in a similar manner.
Zur klassischen Kontaktaufgabe der Elastostatik
Authors: Jentsch Lothar
Published: December 2016

For the study of boundary contact problems of thermoelastostatics, thermoelastic vibrations and other models with boundary integral methods the main difficulty which arises is, that displacement and stress contact conditions are to fulfil on the contact-surface between the elastic homogeneous parts. To solve these difficulties one is forced to study the contact problem of elastostatics. It is proved that an earlier potential representation is proper for getting some better results: 1. The boundary integral operator

\mathcal K

of the contact problem is invertible without any assumption on the Poisson rations of the elastic parts. 2.

\mathcal K

is a strongly elliptic pseudodifferential operator of order zero. Therefore theorems on asymptotic error estimates for boundary element methods are applicable.
On the Singular Behaviour of Fluid in a Vertical Wedge
Authors: Miersemann Erich
Published: December 2016

Solutions of capillary surface equation over domains with corners are considered. It is assumed that the corner is bounded by curves which make an interior angle

2\alpha

with

0 < 2\alpha < \pi

and

\alpha + \gamma < \pi /2

, where

\gamma, 0 < \gamma > \pi /2

is the contact angle between the surface and the container wall. An asymptotic formula for the solutions near the corner is given.
Minimalflächen auf Möbius-Bändern
Authors: Schüffler Karlheinz
Published: December 2016

We develope a global analytic theory for non-orientiable minimal surfaces of the topological type of the Möbius strip. By function-theoretic methods it is possible to give the bundles of harmonic mappings and minimal surfaces including a variation of the conformal type. As an application we prove the so-called "index theorem for minimal surfaces" which in turn implies generic stability and isolatedness of the solutions of the Plateau problem.
On a Lattice Problem for Geodesic Double Differential Forms in the $n$-Dimensional Hyperbolic Space
Authors: Schuster Reinhard
Published: December 2016

Generalizing a lattice point problem we solve a lattice problem for geodesic double differential forms in the

n

-dimensional hyperbolic space. Thereby we use a properly discontinuous group

\mathfrak G

of isometrics of

\mathbb H_n

with compact fundamental domain. We study the relation between lattice sums and the eigenvalue spectrum of the Laplace operator for

p

-forms on the hyperbolic space form

\mathbb H_n/\mathfrak G

. Our approach essentially uses mean value operators for differential forms, their kernel double differential forms and a Landau difference method.
On the approximate solution of elliptic pseudodifferential equations on a smooth closed curve
Authors: Amosov Boris A.
Published: December 2016

We present a procedure for the numerical treatment of elliptic pseudodifferential equations on smooth closed curves using the parametrix for the corresponding pseudodifferential operators combined with the trigonometric collocation procedure. This requires

O(N \mathrm {In} N)

significant operations to find

N

coefficients of the trigonometric polynomial which approximates the solution. We prove that the asymptotic error estimate obtained, including the quadrature errors, is of optimal order in the scale of Sobolev spaces.
Integration by Means of Riemann Sums in Banach Spaces II
Authors: Erben Wolfgang , Grimeisen Gerhard
Published: December 2016

The discussion of the

(\mu, \mathcal X)

-integral introduced in Part I is continued: We investigate the relationship of this integral to the Haupt-Aumann-Pauc integral, the Pettis integral and the Bochner integral. Furthermore, we deal with the representation of iterated integrals as limits of filtered families of iterated Riemann sums.
On Asymptotics of the Green Function and Poisson Kernels of a Mixed Parabolic Problem in a Cone II (in Russian)
Authors: Kozlov Vladimir
Published: December 2016

General boundary value problems for

2b

-parabolic equations in a multidimensional cone are considered. Pointwise estimates as well as asymptotics near the vertex of the cone and as

t \to \infty

are obtained for the Green functions and the Poisson kernels.
Quadrature Formula, FEM-Approximation (in Russian)
Authors: Michlin S.G.
Published: December 2016

The author has constructed in one of his preceeding papers a FEM-approximation formula for functions of the class

C^{(s)} [0, 1]

(

s

an arbitrary natural number) which depends only on the values of the given function at the knots of the net. This construction demands to continue the given function (with preserving the class

C^{(s)}

on a little segment of one or both sides of the segment [0, 1]. Accordingly one obtains two approximate formulae. Integrating them one obtains two quadrature formulae which accuracy depends from

s

. The right-hand side of every of them is the sum of the right-hand side of the classical trapezoid rule and some boundary layer. If one use bilateral continuation, then the boundary layer becomes a little more complicated, but the accuracy of the quadrature formula increases.
On the Linearization of the Satsuma-Mimura Diffusion Equation in the Spatial Periodic Case
Authors: von Wolfersdorf Lothar
Published: December 2016

For the solution of the diffusion equation of Satsuma and Mimura in the spatially periodic case general formulae are given. Furthermore some simple criteria for existence and non-existence of the solution for all times are derived and illustrated by examples.
Paley-Wiener-Sätze auf kompakten topologischen Gruppen
Authors: Bauch Hans F.
Published: December 2016

The connection between analyticity of functions on a compact connected group and the properties of their Fourier coefficients is lnvestigated.The functions with exponentially rapidly decreasing Fourier coefficients are exactly the analytic vectors of the right regular representation with the representation space of the functions with absolutely convergent Fourier series.They also can be continued analytically in the complexification of the group.
Abelsche Sätze für die Laplace-Transformation von Distributionen
Authors: Glaeske Hans-Jürgen , Müller Dietmar
Published: December 2016

The notion of similarity of distributions as

x \to 0+

and

x \to + \infty

, respectively, is defined and by means of this idea well-known Abelian theorems for the Laplace transform are transfered to that one of distributions.
On the numerical solution of pseudoparabolic equations
Authors: Lundin Leroy R. , Lundin Leroy R.
Published: December 2016

In this work the authors find discrete analogues of the fundamental singularities for pseudo-parabolic equations. The method developed by Colton and Gilbert for analytic coefficients is used to motivate the approach. Indeed, the finite difference Green’s function is seen to play the same role here as in the analytic case. The method of lines is employed to treat the time differentiation. Furthermore, error estimates are obtained which compare the continuous solutions to the finite difference approximations.
On Structure Preserving Transformations in Hamiltonian Control Systems
Authors: Abesser Harald , Steigenberger Joachim
Published: December 2016

Hamiltonian control systems with natural output in the sense of [12] are considered. We investigate state-dependent co-ordinate transformations in the space of controls

u

and observables

y

which preserve the Hamiltonian structure.These transformations can be characterized and constructed by canonical transformations in the (

y, u

)-pace.The results generalize known statements on Hamiltonian systems affine in the control and hold for general gradient-like control systems as well.
Stability of Nonlinear Systems with Periodically Nonstationary Linear Part
Authors: Yakubovich V.A.
Published: December 2016

Multidimensional nonlinear systems with periodically nonstationary linear part are considered. It is supposed that nonlinear blocks satisfy some integral quadratic constraint. The necessary and sufficient condition of absolute stability with respect to output for such systems are established in terms of certain properties of solutions of a linear Hamiltonian system with periodic coefficients. In the case of constant coefficients this condition transforms into a well-known frequency criterion of absolute stability.
On the Periodic Solution Process to the Stochastic Model of Single Species
Authors: Shen Yuyi , Zhang Binggen
Published: December 2016

Two stochastic models of single species are studied. A necessary and sufficient condition and a sufficient condition for existence of the periodic solution process are obtained, respectively.
On a Boundary Value Problem for a Special Class of First Order Semilinear Elliptic Systems in the Plane
Authors: von Wolfersdorf Lothar
Published: December 2016

By means of known results of Brezis and Browder on integral equations of Hammerstein type existence theorems for a class of Riemann–Hilbert problems for Vekua’s differential equation systems with power-like nonlinearity are proven.
Determination of a Real Parameter in the Coefficient of a Quasilinear Elliptic Differential Equation
Authors: Handrock-Meyer Sybille
Published: December 2016

We study the quasilinear elliptic differential equation

\mathrm {div}((b(u–u_o)^1 + c) \mathrm {grad}u) = 0

with boundary value conditions of Dirichlet type in an

n

-dimensional cylinder. Provided we know the numbers

u_o

,

I

and

c

, the solution u on a plane which is parallel to the basic area of the cylinder, an eigenvalue and an eigenfunction of a certain eigenvalue problem, we give an explicit formula for the calculation of the real parameter

b

.
Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmungsform
Authors: Duzaar Frank , Fuchs Martin
Published: December 2016

Given an integral

m

-current

T_o

in

\mathbb R^{m+k}

and a tensor

H

of type

(m,1)

on

\mathbb R^{m+k}

with values orthogonal to each of its arguments we prove under suitable smallness conditions the existence of an integral

m

-current

T

with boundary

\partial T = \partial T_o

aI having prescribed mean curvature form

H

.
Asymptotic Expansions for Regularization Methods of Linear Fully Implicit Differential-Algebraic Equations
Authors: Hanke Michael
Published: December 2016

Correction to the paper in Z. Anal. Anw. 13 (1994)3, 513 - 535. Caused by a regrettable error of the editors, in the above paper on p. 521 two figures were missing.
The Comparison of Two Error Estimates for Approximate Solutions of the Poisson Equation
Authors: Lüttgens Gerald
Published: December 2016

The purpose of the present paper is to discuss different error estimates for the numerical solution of a Dirichlet problem for the Poisson equation, calculated via the five point (discrete) Laplacian. Whereas the first error bound, a sum of ordinary

L^\infty

-moduli, is deduced from the usual stability inequality, use is made of some properties of the discrete Green function to verify another stability inequality in terms of

l^1

-norms, which then implies the second estimate via

\tau

-moduli multiplied by a logarithm factor. In the following we will show that it depends on the solution of the boundary value problem which measure of smoothness or rather which error estimate delivers the correct rate of convergence. The paper concludes with some remarks illustrating relations to the well-known logarithm factor in connection with finite element approximation.
Nonlinear Elliptic Equations Involving Critical Sobolev Exponents: Asymptotic Analysis via Methods of Epi-Convergence
Authors: Bandle Catherine , Brillard A.
Published: December 2016

We study the minimizers of two functionals involving critical Sobolev exponents, and whose Euler equations lead to nonlinear boundary value problems. We first employ classical methods to obtain estimates. We then rephrase the problems in a more abstract functional analytical setting. We use epi-convergence arguments in order to describe the behaviour of the minimizers.
Dualität bei Steuerungsproblemen und zugeordneten Flussproblemen II
Authors: Klötzler Rolf
Published: December 2016

In this paper a duality is presented for problems of optimal control with multiple integrals. The same is performed for related more-dimensional flow problems which are generated from the first problems by a relaxing procedure (as in the one-dimensional case according to Part I). Both of these optimization problems have the same dual problem. For flow problems one can prove the validity of strong duality by means of Rockafellars Duality Theory under some additional assumptions.
Asymptotic Expansions for Regularization Methods of Linear Fully Implicit Differential-Algebraic Equations
Authors: Hanke Michael
Published: December 2016

Differential-algebraic equations with a higher index can be approximated by regularization algorithms. One of such possibilities was introduced by März for linear time varying index 2 systems. In the present paper her approach is generalized to linear time varying index 3 systems. The structure of the regularized solutions and their convergence properties are characterized in terms of asymptotic expansions. In this way it is also possible to characterize the so-called pencil regularization in the index 2 case.
Maximale Strömungen vollergodischer Automorphismen mit quasidiskretem Spektrum
Authors: Weihert Edwin
Published: December 2016

Every totally ergodic automorphism with quasi-discrete spectrum on a Lebesgue space can be embedded in a maximal discrete flow which is generated by all roots of the automorphism. It is also shown that for every subgroup of the additive group of the rationals and every natural

n

a totally ergodic automorphism with quasidiscrete spectrum exists which Halmos-invariant is equal to

n

and which can be embedded in a discrete flow which parametergroup is the given subgroup of the rationals.
$L_{\varphi}$-Spaces and some Related Sequence Spaces
Authors: Boos Johann , Grosse-Erdmann Karl-Goswin , Leiger T.
Published: December 2016

In view of closed graph theorems in case of maps defined by operator-valued matrices

L_{\varphi}

-spaces were recently introduced by two of the present authors as a generalization of separable

FK(X)

-spaces. In this paper we study the class of

L_{\varphi}

-spaces and a few closely related classes of sequence spaces. It is shown that an analogue of Kalton’s closed graph theorem holds for matrix mappings if we consider

L_{\varphi}

-spaces as range spaces, and paralleling a result of Qiu we prove that the class of

L_{\varphi}

-spaces is the best-possible choice here. As a consequence we show that for any

L_{\varphi}

-space

E

every matrix domain

E_A

is again an

L_{\varphi}

-space.
Perron’s Method and Barrier Functions for the Viscosity Solutions of the Dirichlet Problem for some Non-Linear Partial Differential Equations
Authors: Ramaswamy Mythily , Ramaswamy S.
Published: December 2016

The Dirichlet problem for some non-linear partial differential equations via Perron’s method is studied in the viscosity set up, by considering two families of functions, instead of one, as considered by others before. The notion of barrier at a boundary point is introduced to study the regularity of boundary points. Barriers for some non-linear operators are also constructed.
On Stationary Incompressible Norton Fluids and some Extensions of Korn’s Inequality
Authors: Fuchs Martin
Published: December 2016

A simple mathematical model for a so-called Norton fluid is given. We study a variational problem and make use of appropriate versions of Korn’s inequality.
Estimating Remainder Functionals by the Moduli of Smoothness
Authors: Köhler P.
Published: December 2016

For remainder functionals (e.g., approximation or quadrature errors), estimates by the moduli of smoothness are obtained. As a by-product, the constants in the estimate of the

\mathcal K

-functional by the moduli of smoothness are improved.
Location of the Complex Zeros of Bessel Functions and Lommel Polynomials
Authors: Ifantis E.K. , Kokologiannaki C.G.
Published: December 2016

Some inequalities for the complex zeros of Bessel functions and the zeros of Lommel polynomials, which improve previously known results, are presented.