- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 11:23:01
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=5&iss=1&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)
5
1986
1
A Theory of Quantum Measurement Based on the CCR Algebra L$^+(\mathcal W)$
Daniel
Dubin
Open University, MILTON KEYNES, UNITED KINGDOM
J.
Sotelo-Campos
Open University, MILTON KEYNES, UNITED KINGDOM
Starting from L$^+(\mathcal W)$ as the algebra of observables, $\mathcal W$ a space of type $\mathcal S$, a theory of quantum measurement is devised. It is based on the theory of Davies and Lewis, but adapted to unbounded symmetric operators defined on a common dense domain and no restriction on the spectra.
General
1
26
10.4171/ZAA/176
http://www.ems-ph.org/doi/10.4171/ZAA/176
Universale Rettungskurven I
Rolf
Klötzler
, BORSDORF, GERMANY
Object of this paper is the search for a curve of minimal length and with the property by arbitrary starting directions to join each point and the shore of any lake with given thickness. In part I the unique solution (apart from congruence) is found by means of duality in optimal control and a special structure hypothesis.
General
27
38
10.4171/ZAA/177
http://www.ems-ph.org/doi/10.4171/ZAA/177
Zur Regularität schwacher Lösungen thermoelastischer Variationsprobleme für stückweise stetige, anisotrope Körper unter Kopplungsbedingungen
Regina
Funke
, LEIPZIG, GERMANY
There are studied regularity properties of weak solutions of variational problems of thermoelasticity for anisotropic, heterogeneous bodies under coupling conditions along the surfaces of discontinuity.
General
39
45
10.4171/ZAA/178
http://www.ems-ph.org/doi/10.4171/ZAA/178
Ein Regularitätssatz für ein lineares System von Variationsungleichungen mit einer Halbraumnebenbedingung
Martin
Fuchs
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
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.
General
47
57
10.4171/ZAA/179
http://www.ems-ph.org/doi/10.4171/ZAA/179
Approximation by Solutions of Elliptic Equations
Uwe
Hamann
Universität Rostock, ROSTOCK, GERMANY
Günther
Wildenhain
Universität Rostock, ROSTOCK, GERMANY
Let $\Omega \subset \mathbb R^n$ be a bounded, smooth domain, $\Gamma$ a closed, smooth, $(n-1)$-dimensional surface with boundary in the interior of $\Omega$ and $V$ an open subset of the boundary $\partial \Omega$. In $\Omega$ we consider a properly elliptic differential operator $L$ of order $2m$ with smooth coefficients. Let $(B_1, \dots, B_m)$ be normal system of boundary operators on $\partial \Omega$, which fulfils the classical root condition. $L_V(\Gamma)$ denote the space of the restrictions on $\Gamma$ of the functions from $$L_V(\Omega) = \{u \in C^\infty \Omega \colon Lu = 0 \; \mathrm {in}\; \Omega, \; B_1u|_{\partial \Omega} = \cdots = B_mu|_{\partial \Omega} = 0 \; \mathrm {in} \; \partial \Omega \; \backslash \; V\}.$$ It is proved that $L_V(\Gamma)$ is dense in the space $W_p^{2m-1/p} (\Gamma) (p > 1)$.
General
59
69
10.4171/ZAA/180
http://www.ems-ph.org/doi/10.4171/ZAA/180
Eine Parallelogrammungleichung zum Exponenten $\gamma \in [1, 2]$ für Normen
Armin
Hoffmann
TU Ilmenau, ILMENAU, GERMANY
For a Hilbert space $X$ the generalized parallelogramm inequality to the exponent $\gamma$ $$\lambda \| x_1 \|^\gamma + (1-\lambda) \|x_2\| \leq \|\lambda x_1 + (1-\lambda) x_2\|^\gamma + \mathrm {min} \{ \lambda, 1-\lambda\} C (\gamma) \|x_1 - x_2\|^\gamma$$ for every $x_1, x_2 \in X, \lambda \in [0,1], \gamma \in [1,2]$ is proved and the constant $C(\gamma)$ is determined. The extension of this inequality to certain normed spaces is possible with restrictions of the parameter $\gamma$.
General
71
83
10.4171/ZAA/181
http://www.ems-ph.org/doi/10.4171/ZAA/181
On Strong Unboundedness of Symmetric Operators
Jürgen
Friedrich
Universität Leipzig, LEIPZIG, GERMANY
It will be shown that for each positive odd integer $n$ there is a symmetric operator $\mathcal T$ in a separable Hilbert space $\mathcal H$ such that $\mathcal T, \mathcal T^3, \dots, \mathcal T^n$ are unbounded from below and $\mathcal T^k \geq 0$ for $k>n$.
General
85
89
10.4171/ZAA/182
http://www.ems-ph.org/doi/10.4171/ZAA/182