- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 12:55:14
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=3&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)
3
1984
3
Fredholmness and finite section method for Toeplitz operators in $l^p (Z_+ \times Z_+)$ with piecewise continuous symbols II
Albrecht
Böttcher
Technische Universität Chemnitz, CHEMNITZ, GERMANY
In this paper we prove sufficient conditions for Fredholmness of discrete Toeplitz operators with piecewise continuous symbols on the space $l^p$ over the quarter-plane and for the applicability of the finite section method to such operators. The methods used here are based on a bilocalization technique and the local principle of Douglas and Krupnik. Part I of this work contained the proofs of the necessity of the corresponding conditions, the necessary definitions, and the formulation of the main results.
General
193
202
10.4171/ZAA/100
http://www.ems-ph.org/doi/10.4171/ZAA/100
Eine Verallgemeinerung der Lambert-Transformation (II)
Hans-Jürgen
Glaeske
Friedrich-Schiller-Universität Jena, JENA, GERMANY
K.
Stallknecht
Friedrich-Schiller-Universität Jena, JENA, GERMANY
In this paper an inversion formula is proved for the generalized Lambert-transformation which was introduced by the authors in part (I). The proof is possible by means of the representation of this transformation as a Laplace-Stieltjes-transformation, the representation of the Laplace-Stieltjes-transformation as a sum of generalized Lambert transformations and reverse.
General
203
211
10.4171/ZAA/101
http://www.ems-ph.org/doi/10.4171/ZAA/101
Asymptotische Entwicklungen der hypergeometrischen Funktionen $F(a, b, c; z)$ für $|a| \to \infty$ und konstante $b, c, z$
Eberhard
Wagner
Martin-Luther-Universität Halle-Wittenberg, HALLE, GERMANY
Asymptotic expansions of the hypergeometric function $F(a, b, c; z)$ for $|a| \to \infty$ are derived where $b, c (c \neq 0, -1, -2, \dots)$ and $z (z \neq 0, |Arg (1— z)| < \pi)$ are fixed complex numbers.
General
213
226
10.4171/ZAA/102
http://www.ems-ph.org/doi/10.4171/ZAA/102
Über Grundlösungen von Differenzenoperatoren
Eckehard
Pfeifer
Technische Universität Dresden, DRESDEN, GERMANY
Angela
Rauhöft
Technische Universität Dresden, DRESDEN, GERMANY
The method to solve problems of the mathematical physics using the so-called fundamental solutions and its properties is well-known. There is the question how does it work in the case of finite difference equations approximating the mentioned problems. An answer can be given treating difference equations as functional equations in certain spaces of distributions. By a suitable construction it is shown that every linear forward difference operator with constant coefficients possesses a tempered fundamental solution in a neighbourhood (with respect to the discretisation parameter) of the fundamental solution of the corresponding differential operator. An initial-value problem for the one-dimensional equation of heat conduction as an example for a useful application of discrete fundamental solutions closes the paper.
General
227
236
10.4171/ZAA/103
http://www.ems-ph.org/doi/10.4171/ZAA/103
The Laguerre Transform of some Elementary Functions
Hans-Jürgen
Glaeske
Friedrich-Schiller-Universität Jena, JENA, GERMANY
Oleg
Maričev
Belarusian State University, MINSK, BELARUS
This paper deals with the calculation of the generalized Laguerre transformation of a class of functions, which often appear in applications. The result is used for the derivation of the solution of an ordinary differential equation.
General
237
244
10.4171/ZAA/104
http://www.ems-ph.org/doi/10.4171/ZAA/104
Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume
Klaus-Detlef
Kürsten
Universität Leipzig, LEIPZIG, GERMANY
Let $(E_i)_U$ be the ultraproduct of ordered Banach spaces and let $L$ be a finite dimensional sub-space of the dual $(E_i)_u*$. Then there exists a positive iscmetric imbedding of $L$ into $(E_i*)_U$ also satisfying some additional conditions In the case of Banach lattices the isometric imbedding may be chosen as a lattice homomorphism. Similar but somewhat weaker positivity properties can be satisfied for the almost isometric imbeddings of finite dimensional subspaces of $E**$ into $E$ which exist by the principle of local reflexivity.
General
245
262
10.4171/ZAA/105
http://www.ems-ph.org/doi/10.4171/ZAA/105
Zur Vollständigkeit des Systems der Eigenfunktionen irregulärer Eigenwertprobleme mit $\lambda$-abhängigen Randbedingungen
Gerhard
Freiling
Universität Duisburg-Essen, DUISBURG, GERMANY
We show that the system of eigen- and associated functions of the eigenvalue problem $$y^{(n)} + \sum \limits^{n}_{v=2} p_v (x) y^{(n-v)}) = \lambda y \quad 0 \leq x \leq 1,$$ $$U_v (y, \lambda) = 0, \quad 1 \leq v \leq n,$$ with irregular two-point boundary conditions depending on $\lambda$ is complete in $L_2[0,1]$.
General
263
269
10.4171/ZAA/106
http://www.ems-ph.org/doi/10.4171/ZAA/106
Parabolische Regularisierung einer hyperbolischen Itogleichung
Wilfried
Grecksch
Universität Halle-Wittenberg, HALLE, GERMANY
The solution of the first boundary value problem of a random hyperbolic equation is approximated by a method of the parabolic regularization. Considered an application of this method to the development of a maximum principle and to the existence of the $\epsilon$-optimal controls of an optimal control problem of a random hyperbolic equation.
General
271
284
10.4171/ZAA/107
http://www.ems-ph.org/doi/10.4171/ZAA/107