- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 13:00:57
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=7&iss=1&update_since=2024-03-28
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
7
1988
1
On Commutators in Algebras of Unbounded Operators
Werner
Timmermann
Technische Universität Dresden, DRESDEN, GERMANY
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.
General
1
14
10.4171/ZAA/278
http://www.ems-ph.org/doi/10.4171/ZAA/278
On a Singular Part of an Unbounded Operator
Schôichi
Ôta
Kyushu Institute of Design, FUKUOKA, JAPAN
The singularity of an operator in a Hilbert space is studied.
General
15
18
10.4171/ZAA/279
http://www.ems-ph.org/doi/10.4171/ZAA/279
The Conditional Lindeberg–Trotter Operator in the Resolution of Limit Theorems with Rates for Dependent Random Variables. Applications to Markovian Processes
Paul
Butzer
Rheinisch-Westfälische Technische Hochschule Aache, AACHEN, GERMANY
Heribert
Kirschfink
Rheinisch-Westfälische Technische Hochschule Aache, AACHEN, GERMANY
Making use of the properties of conditional expectations, a conditional Lindeberg–Trotter-operator is defined which extends the properties of the classical Lindeberg–Trotter operator to the case of dependent random variables. This approach enables one to establish general limit theorems equipped with little-$\mathcal o$ and large-$\mathcal O$ rates for sums of dependent random variables; these are applied to several versions of the central limit theorem, the weak law of large numbers, and especially to Markovian processes, not only in the case of weak convergence in distribution but partially also for strong convergence.
General
19
39
10.4171/ZAA/280
http://www.ems-ph.org/doi/10.4171/ZAA/280
On $\mathcal B_{p,k}$-Boundedness and Compactness of Linear Pseudo-Differential Operators
Jouko
Tervo
University of Kuopio, KUOPIO, FINLAND
Boundedness and compactness arguments in the Hörmander spaces $\mathcal B_{p,k}$ for linear pseudo-differential operators $L(X, D)$ are considered. The symbol $L(x, \xi)$ of $L(X, D)$ is assumed to obey appropriate temperate criteria, which guarantee that $L(X, D)$ maps the Schwartz class $\mathcal S$ into itself and,that the formal transpose $L’(X, D): \mathcal S \to \mathcal S$ exists. A characterization for the boundedness of the operator $L’(X, D): \mathcal B_{1,kk} \tilde \to \mathcal B_{1,k}$ is obtained. A sufficient condition for the boundedness of the operator $L’(X, D): \mathcal B_{p,kk} \sim \to \mathcal B_{p,k}$ with $p \in [1, \infty]$ is established as well. Finally, the compactness of the continuous extension of $L’(X, D): \mathcal B_{p,kk} \sim (G) \to \mathcal B_{p,k}$ is studied, where $G$ is an open bounded set in $\mathbb R^n$ and where $\mathcal B_{p,kk} \sim (G)$ is (essentially) the completion of $C_0^{\infty} (G)$ with respect to the $\mathcal B_{p,kk} \sim$-norm.
General
41
56
10.4171/ZAA/281
http://www.ems-ph.org/doi/10.4171/ZAA/281
A Free Boundary Value Problem Modeling Thermal Oxidation of Silicon
K.
Gröger
Karl-Weierstraß-Institut für Mathematik, BERLIN, GERMANY
N.
Strecker
Karl-Weierstraß-Institut für Mathematik, BERLIN, GERMANY
Using results on evolution equations in Hilbert spaces a problem describing the diffusion of an oxidant through an oxide layer and the growth of this layer caused by the oxidation of silicon is solved. Moreover, estimates for the growth of the thickness of the oxide layer being of practical interest are given.
General
57
66
10.4171/ZAA/282
http://www.ems-ph.org/doi/10.4171/ZAA/282
Gieichgewichtsfiguren magnetischer Flüssigkeiten
Klaus
Beyer
Universität Leipzig, LEIPZIG, GERMANY
Equilibrium configurations of magnetic liquid drops subject to an applied magnetic field and to surface tension are investigated. Existence and uniqueness of such configurations in the neighbourhood of a sphere in sufficiently weak fields are proved.
General
67
76
10.4171/ZAA/283
http://www.ems-ph.org/doi/10.4171/ZAA/283
On the Elliptic Sturmian Theory for General Domains
Erich
Müller-Pfeiffer
Pädagogische Hochschule, ERFURT, GERMANY
The well-known comparison theorem by Sturm and Picone for ordinary, self-adjoint, second order differential equations is extended to self-adjoint elliptic differential equations. The basic domain $G$ and the coefficients of the equation are not necessarily bounded, and no regularity hypotheses on the boundary $\partial G$ are required.
General
77
83
10.4171/ZAA/284
http://www.ems-ph.org/doi/10.4171/ZAA/284
A Variational Principle for General Polymer Systems
Volker
Warstat
Universität Halle-Wittenberg, HALLE, GERMANY
A new model for classical statistical mechanics of interacting extended particles (polymers) is introduced. First, the construction of the configuration space for polymer systems is given. Then the existence of the thermodynamic limit of the local pressure is derived. For this limit which is called the pressure of the system a variational principle is proved. Finally, for given interaction, the class of equilibrium states determined by this variational principle is proved to coincide with the class of translation invariant Gibbs states.
General
85
93
10.4171/ZAA/285
http://www.ems-ph.org/doi/10.4171/ZAA/285