- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 15:52:57
10
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=4&iss=3&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)
4
1985
3
Generalization of Cramér’s and Linnik’s Factorization Theorems in the Continuation Theory of Distribution Functions
H.-J.
Rossberg
Universität Leipzig, LEIPZIG, GERMANY
Stimulated by a problem of Kruglov and a result of Titov we derive an elementary continuation theorem for distribution functions. It implies the following generalization of Carmér’s theorem. Let $F_1$ and $F_2$ be two non-degenerate distribution functions such that $$F_1 \ast F_2(x) = \Phi_{a, \sigma}(x), \quad \quad x \leq x_0$$ where $x_0 \in \mathbb R_1$ and $\Phi_{a, \sigma}$ stands for the normal distribution $N(a, \sigma^2)$; if the corresponding characteristic functions $f_1$ and $f_2$ do not vanish in the upper half plane, then $F_1$ and $F_2$ are also normal. Linnik’s theorem can be analogously generalized. More general variants are also discussed.
General
193
200
10.4171/ZAA/144
http://www.ems-ph.org/doi/10.4171/ZAA/144
Über die Struktur maximaler Ideale in LMC*-Algebren
Marlen
Fritzsche
Universität Potsdam, POTSDAM, GERMANY
We describe the structure of dense maximal left ideals for the simplest non-commutative LMC*-algebras. Further we show, for these examples, that the correspondence "dense maximal left ideals $\to$ extremal states of the bounded part of the algebra, not extendable to continuous states of the whole algebra" is not one-to-one as in the commutative case.
General
201
205
10.4171/ZAA/145
http://www.ems-ph.org/doi/10.4171/ZAA/145
A Note on Optimal Domains in a Reaction-Diffusion Problem
Catherine
Bandle
, AESCH/BL, SWITZERLAND
A simple model for a chemical reaction is considered. The vessel where the reaction takes place is optimal if no dead core appears and if effectiveness is high. By means of the method of upper and lower solutions it is shown that, independent of the volume, sufficiently thin domains have this property. The proof is based on an estimate for the solution of the Dirichlet problem.
General
207
213
10.4171/ZAA/146
http://www.ems-ph.org/doi/10.4171/ZAA/146
Das Poincarésche Randsteuerproblem bei elliptischen Differentialgleichungen zweiter Ordnung
Dieter
Oestreich
Hochschule für Technik und Wirtschaft Dresden, DRESDEN, GERMANY
There are considered the Poincaré boundary control problem for elliptic differential equations of second order and a mixed Riemann-Hilbert control problem with generalized analytic functions, where the control occurs non-linearly in the coefficients of the boundary condition or the differential equation too. Existence theorems are proved for these problems with integral cost functions, constraints and additional conditions.
General
215
224
10.4171/ZAA/147
http://www.ems-ph.org/doi/10.4171/ZAA/147
Automatische Steuerung freier Ränder bei Stefan-Problemen durch Thermostatkontrollen am festen Rand
Karl-Heinz
Hoffmann
Technische Universität München, MÜNCHEN GARCHING, GERMANY
H.-J.
Kornstaedt
Freie Universität Berlin, BERLIN, GERMANY
Jürgen
Sprekels
Angewandte Analysis und Stochastik, BERLIN, GERMANY
The automatic control of the free boundary in one-phase Stefan problems via the input data at the fixed boundary is considered. In contrast to previous papers concerned with this subject the thermostat controlling the input data observes the temparature at the fixed boundary instead of the evolution of the free boundary. The corresponding parabolic initial-boundary value system is nonlinear and discontinuous. Unique solvability is shown and numerical results are presented.
General
225
233
10.4171/ZAA/148
http://www.ems-ph.org/doi/10.4171/ZAA/148
Riemannian Manifolds for which a Power of the Radius is $k$-harmonic
Rainer
Schimming
Ernst-Moritz-Arndt-Universität Greifswald, GREIFSWALD, GERMANY
Let $\sigma = \sigma (x, y)$ denote Synge’s function of a Riemannian manifold $(M, g)$ of any signature and consider the condition that some power of $\sigma$ or the logarithm of $\sigma$ is $k$-harmonic. Then in many, cases $(M, g)$ turns out to be flat. Certain classes of non-flat manifolds can be characterized just by a condition of the aforesaid typo.
General
235
249
10.4171/ZAA/149
http://www.ems-ph.org/doi/10.4171/ZAA/149
A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order
Erich
Müller-Pfeiffer
Pädagogische Hochschule, ERFURT, GERMANY
St.
Werler
Pädagogische Hochschule, ERFURT, GERMANY
Self-adjoint differential operators of order $2n$ are considered that are associated with the expression $\mathcal A \equiv w^{-1} [(—1)^n (py^{(n)})^{(n)} + qy]$ and the weighted Hilbert space $L_{2, w}(0, \infty)$. By use of discreteness conditions for the spectrum of such operators given by Kwong and Zettl a necessary and sufficient condition for the discreteness of the spectrum is established.
General
251
256
10.4171/ZAA/150
http://www.ems-ph.org/doi/10.4171/ZAA/150
Laplace-Gauss Integrals, Gaussian Measure Asymptotic Behaviour and Probabilities of Moderate Deviations
Wolf-Dieter
Richter
Universität Rostock, ROSTOCK, GERMANY
There is given a general Gaussian measure representation on arbitrary finite dimensional Borel sets. This representation reflects B. Cavalieri’s and E. Torricelli’s "indivisible method" in a modern language. Based upon it, assertions are derived about the Gaussian measure asymptotic behaviour on Borel sets whose distance from the origin tends to infinity. Also two specific multivariate moderate deviation limit theorems for sums of i.i.d. random vectors are deduced.
General
257
267
10.4171/ZAA/151
http://www.ems-ph.org/doi/10.4171/ZAA/151
Vergleichende Betrachtungen zur Bestimmung des asymptotischen Verhaltens mehrdimensionaler Laplace-Gauss-Integrale
Hartmut
Birndt
Technische Universität Dresden, DRESDEN, GERMANY
Wolf-Dieter
Richter
Universität Rostock, ROSTOCK, GERMANY
The asymptotic behaviour of the Gaussian measure is investigated for some Borel sets in which one is interested in the theory of probabilities of large deviations and the distance of which from the origin tends to infinity. To that end, various methods for studying Laplace-Gauss integrals are compared. Some new assertions are illustrated by many examples.
General
269
276
10.4171/ZAA/152
http://www.ems-ph.org/doi/10.4171/ZAA/152
Ritz-Regularization versus Least-Square-Regularization. Solution Methods for Integral Equations of the First Kind
E.
Schock
Universität Kaiserslautern, KAISERSLAUTERN, GERMANY
Three principles of regularization methods are discussed (Tikhonov-, Ritz- and Galerkin-method), and it is shown that in the case of positive definite or of selfadjoint operators the Ritz- and the Galerkin-principles (the latter with non-real parameter) have better properties than the Tikhonov-principle.
General
277
284
10.4171/ZAA/153
http://www.ems-ph.org/doi/10.4171/ZAA/153