- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:03:45
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=11&iss=4&update_since=2024-03-29
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)
11
1992
4
Products of Distributions in Several Variables and Applications to Zero–Mass QED$_2$
Hans
Embacher
Universität Innsbruck, INNSBRUCK, AUSTRIA
Gebhard
Grübl
Universität Innsbruck, INNSBRUCK, AUSTRIA
Michael
Oberguggenberger
Universität Innsbruck, INNSBRUCK, AUSTRIA
Products of distributions, renormalization, Wightman distributions
We study products of distributions in several variables, having in mind applications to quantum electrodynamics. We introduce a new product, the parameter product, and relate it to known ones. It allows us to rigorously interpret and evaluate products arising in the computations of the one-loop vacuum polarization of zero-mass QED$_2$ , thereby avoiding the occurrence of renormalization ambiguities from the very beginning.
Functional analysis
Quantum theory
437
454
10.4171/ZAA/591
http://www.ems-ph.org/doi/10.4171/ZAA/591
A Study on the Geometry of Pairs of Positive Linear Forms, Algebraic Transition Probability and Geometrical Phase over Non-Commutative Operator Algebras (II)
Peter
Alberti
Universität Leipzig, LEIPZIG, GERMANY
Functional analysis, $C*$-algebras, $vN$-algebras, non-commutative probability, non-commutative geometry
The results of the first part [1] will be used to discuss and to investigate some extensions of geometrical notions, which recently have been found to be of interest in Mathematical Physics in context of the problems of the so-called geometrical phase. The concepts of the global phase, the phase group and holonomy group of a normal state of a $vN$-algebra will be introduced and discussed.
Functional analysis
455
488
10.4171/ZAA/590
http://www.ems-ph.org/doi/10.4171/ZAA/590
On Some Completion Problems for Various Subclasses of $j_{pq}$-inner Functions
D.Z.
Arov
South-Ukrainian State Pedagogical University, ODESSA, UKRAINE
B.
Fritzsche
Universität Leipzig, LEIPZIG, GERMANY
B.
Kirstein
Universität Leipzig, LEIPZIG, GERMANY
$j_{pq}$-inner functions, A-singular $j_{pq}$-inner functions, $j_{pq}$-elementary factors, pseudocontinuation
Several completion problems of the following type will be studied: Given meromorphic matrix-valued functions $f$ and $h$, the question is to describe the set of all $j_{pq}$-inner functions $W$ which have the block structure $W = (^{*f}_{*h}9$.
Functions of a complex variable
489
508
10.4171/ZAA/589
http://www.ems-ph.org/doi/10.4171/ZAA/589
On the Flow of a Temperature-Dependent Bingham Fluid in Non-Smooth Bounded Two-Dimensional Domains
H. Ulrich
Kalex
alfabet AG, BERLIN, GERMANY
Bingham fluids, non-smooth domains, temperature-coupled fluid flow
A result on the existence and smoothness of solutions for temperature-coupled Bingham problems in non-smooth bounded 2D-domains is proved, which complements the results of G. Duvaut and J. L. Lions [3] on this subject.
Fluid mechanics
Partial differential equations
509
530
10.4171/ZAA/588
http://www.ems-ph.org/doi/10.4171/ZAA/588
Numerical Solutions for Some Free Boundary Value Problems Occuring in Planar Fluid Dynamics
Leroy
Lundin
University of Delaware, NEWARK, UNITED STATES
Wen
Guochun
Peking University, BEIJING, CHINA
Numerical solutions, free boundary problems
In the paper [1], we consider the solvability of some free boundary value problems occuring in planar fluid dynamics. The object of the present paper is to present numerical methods for solving free boundary problems. It was shown in [1] that such free boundary problems may be transformed into a mixed boundary value problem for a linear or nonlinear elliptic complex equations, which in turn, might be reformulated into a conformal mapping or quasiconformal mapping from a general domain onto some canonical domain. In this paper we direct our discussion to the numerical solution of mixed boundary value problems for generalized Beltrami equations.
Partial differential equations
Numerical analysis
531
537
10.4171/ZAA/587
http://www.ems-ph.org/doi/10.4171/ZAA/587
A Stochastic Nonlinear Evolution Equation
Wilfried
Grecksch
Universität Halle-Wittenberg, HALLE, GERMANY
Stochastic partial differential equations, difference equations
A stochastic evolution equation for processes with values in two orthogonal subspaces of a Hilbert space is considered. Such types of equations arise in the study of quasistatic processes of elastic viscoplastic materials with random disturbances. Using the theory of Hilbert space valued Ito equations an existence and uniqueness theorem is proved. Finally a time discrete approximation is discussed.
Probability theory and stochastic processes
539
552
10.4171/ZAA/586
http://www.ems-ph.org/doi/10.4171/ZAA/586
Boundary Theorems of the Gehring-Lohwater and Plessner Type for Polyanalytic Functions
Mark Benevich
Balk
Pedagogical Institute, SMOLENSK, RUSSIAN FEDERATION
Wolfgang
Tutschke
Technische Universität Graz, GRAZ, AUSTRIA
Boundary properties, polyanalytic functions, inhomogeneous Cauchy-Riemann equation, cluster sets
Using methods of the theory of generalized analytic functions, the present paper investigates the boundary behaviour of non-holomorphic functions (such as polyanalytic ones) provided the areolar derivative $\partial /\partial \bar{z}$ belong to an $L_p$ space, $p > 2$.
Functions of a complex variable
553
558
10.4171/ZAA/585
http://www.ems-ph.org/doi/10.4171/ZAA/585
Sufficiency Conditions for Weak Local Minima in Multidimensional Optimal Control Problems with Mixed Control-State Restrictions
Sabine
Pickenhain
Brandenburgische Technische Universität Cottbus, COTTBUS, GERMANY
Sufficient optimality conditions, multidimensional control problems, parametric optimization
In [13] a new sufficiency criterion for strong local minimality in multidimensional non-convex control problems with pure state constraint was developed. In this paper we use a similar method to obtain sufficient conditions for weak local minimality in multidimensional control problems with mixed state-control restrictions. The result is obtained by applying duality theory for control problems of Klötzler [11] as well as first and second order optimality conditions for optimization problems described by $C^$-functions having a locally Lipschitzian gradient mapping. The main theorem contains the result of Zeidan [17] for one-dimensional problems withoutstate restrictions.
Calculus of variations and optimal control; optimization
559
568
10.4171/ZAA/584
http://www.ems-ph.org/doi/10.4171/ZAA/584