- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:33:18
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=1&iss=3&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)
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1982
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Asymptotische Darstellungen der hypergeometrischen Funktionen für grosse Werte eines Parameters
Eberhard
Wagner
Martin-Luther-Universität Halle-Wittenberg, HALLE, GERMANY
Asymptotic expansions of the hypergeometric function $F(a, b, c; z)$ for $|b| \to \infty$ where $a, c, z$ are fixed complex numbers given in well-known tables (e.g. Bateman/Erdélyi: Higher transcendental functions I. New York 1953) are incorrect. In the present paper asymptotic representations of the hypergeomctric function $F$ for $a$ (complex) $\to \infty$ are derived where $b, c (c \neq 0, -1, -2,\dots)$ and $z (z \neq 0$, |Arg $(1- z) | < \pi$ are fixed complex numbers. By change of $a$ and $b$ appropriate asymptotic representations of $F$ for $|b| \to \infty$ are obtained.
General
1
11
10.4171/ZAA/16
http://www.ems-ph.org/doi/10.4171/ZAA/16
Remarks on quadratic optimal control problems in Hilbert spaces
Hans
Benker
Martin-Luther-Universität Halle-Wittenberg, HALLE, GERMANY
Steffen
Kossert
Technische Hochschule Leuna Merseburg, MERSEBURG, GERMANY
In this paper quadratic optimal control problems in Hilbert spaces are considered. For this problem properties of the optimal control and bounds are given.
General
13
21
10.4171/ZAA/17
http://www.ems-ph.org/doi/10.4171/ZAA/17
Strong solutions of a two-dimensional stochastic Navier-Stokes system and corresponding Kolmogorov equations (in Russian)
Marko
Vishik
Moscow Lomonosov State University, MOSCOW, RUSSIAN FEDERATION
Alexander
Komech
Universität Wien, WIEN, AUSTRIA
A random process governed by a two-dimensional, stochastic Navier-Stokes system with a white noise under periodic boundary conditions is constructed. The solution of the corresponding Kolmogorov forward equation is obtained in the class of exponentially decreasing measures. Furthermore, the generalized solution of the corresponding Kolmogorov backward equation is also constructed. This solution possesses a probabilistic representation as path integral and satisfies a Hölder condition. The generalized solution is defined by the Green identity for the solution of the Kolmogorov forward and backward equations. On any small interval of time this generalized solution of the Kolmogorov backward equation is the classical one.
General
23
52
10.4171/ZAA/18
http://www.ems-ph.org/doi/10.4171/ZAA/18
Solution of a degenerated elliptic equation of second order in an unbounded domain
Werner
Berndt
Universität Leipzig, LEIPZIG, GERMANY
The paper deals with the equation div $(\varrho (x) (\bigtriangledown u + f(x))) = 0$ in $\mathbb R^N$, where $\varrho \in L_1 (\mathbb R^N)$ and $f \in L_2 (\mathbb R^N, \varrho)$ are given smooth functions. The equation degenerates on the smooth surface $\Gamma = \{\varrho (x) = 0\}$ where $\varrho (x)$ behaves like a power of dist $(x, \Gamma)$. The following results are proved: 1. Existence and uniqueness (up to additive constants) of a solution with $\int | \bigtriangledown u|^2 \varrho \mathrm d x< \infty$; the proof uses a variational method in a weighted Sobolev space; 2. Regularity of the solution near $\Gamma$; 3. Convergence and correctness of a numerical (difference) method; 4. Convergence of an iteration method to solve the discrete problem.
General
53
68
10.4171/ZAA/19
http://www.ems-ph.org/doi/10.4171/ZAA/19
On Entropy-Like Invariants for Dynamical Systems
Thomas
de Paly
Universität Leipzig, LEIPZIG, GERMANY
This paper transfers the theory of the Kolmogorov-Sinai-entropy a method which is a basic tool in the theory of the order-structure of states. The function $h(x) = —x$ log $z$ is replaced by arbitrary bounded, concave functions in all definitions of the entropy-theory. This procedure leads to a class of isomorphy invariants, thus generalizing the notion of dynamical entropy. The general properties of the generalized dynamical entropies are investigated and an explicit calculation of the new invariants is accomplished on some simple cases.
General
69
79
10.4171/ZAA/20
http://www.ems-ph.org/doi/10.4171/ZAA/20
On the existence of dense ideals in LMC*-algebras
Marlen
Fritzsche
Universität Potsdam, POTSDAM, GERMANY
In this paper we prove the following proposition: The existence of an unbounded element in an LMC*-algebra (with unity) implies the existence of a dense ideal in this algebra.
General
81
84
10.4171/ZAA/21
http://www.ems-ph.org/doi/10.4171/ZAA/21
Remarks on the dual least action principle
Michel
Willem
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Let $L$ be a self-adjoint operator with a closed range in a Hilbert space $H$ and let $\psi$ be a convex function on $H$. Under a non resonance assumption the surjectivity of $L + \partial \psi$ is studied.
General
85
90
10.4171/ZAA/22
http://www.ems-ph.org/doi/10.4171/ZAA/22