- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:46:18
10
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=10&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)
10
1991
1
Double Walsh Series with Coefficients of Bounded Variation
Ferenc
Móricz
University of Szeged, SZEGED, HUNGARY
Convergence properties of double Walsh series are studied whose coefficients form a null sequence of bounded variation. These series converge regularly at all points of (0, 1) x (0, 1) and converge in the pseudometric of $L^r$ for all $r \in (0, 1)$. Sufficient conditions for convergence are also proved which involve the second-order differences of the coefficients.
Fourier analysis
3
10
10.4171/ZAA/426
http://www.ems-ph.org/doi/10.4171/ZAA/426
Integration by Means of Riemann Sums in Banach Spaces II
Wolfgang
Erben
Hochschule für Technik Stuttgart, STUTTGART, GERMANY
Gerhard
Grimeisen
Universität Stuttgart, STUTTGART, GERMANY
The discussion of the $(\mu, \mathcal X)$-integral introduced in Part I is continued: We investigate the relationship of this integral to the Haupt-Aumann-Pauc integral, the Pettis integral and the Bochner integral. Furthermore, we deal with the representation of iterated integrals as limits of filtered families of iterated Riemann sums.
General
11
26
10.4171/ZAA/427
http://www.ems-ph.org/doi/10.4171/ZAA/427
On Asymptotics of the Green Function and Poisson Kernels of a Mixed Parabolic Problem in a Cone II (in Russian)
Vladimir
Kozlov
Linköping University, LINKÖPING, SWEDEN
General boundary value problems for $2b$-parabolic equations in a multidimensional cone are considered. Pointwise estimates as well as asymptotics near the vertex of the cone and as $t \to \infty$ are obtained for the Green functions and the Poisson kernels.
General
27
42
10.4171/ZAA/428
http://www.ems-ph.org/doi/10.4171/ZAA/428
On a Free Boundary Problem Modelling Thermal Oxidation of Silicon
Guan
Zhicheng
Zhejiang University, HANGZHOU, CHINA
Considering the problem modelling thermal oxidation of silicon as one-phase non-equilibrium problem, we use Schauder’s fixed point theorem to prove the existence and uniqueness of the classical solution.
General
43
48
10.4171/ZAA/429
http://www.ems-ph.org/doi/10.4171/ZAA/429
Approximation durch Lösungen elliptischer Randwertprobleme auf offenen Mengen II
Uwe
Hamann
Universität Rostock, ROSTOCK, GERMANY
General
49
61
10.4171/ZAA/430
http://www.ems-ph.org/doi/10.4171/ZAA/430
Duality for Nonlinear Abstract Evolution Differential Equations
Andrzej
Nowakowski
Uniwersytet Lodzki, LODZ, POLAND
Andrzej
Rogowski
Uniwersytet Lodzki, LODZ, POLAND
The existence of periodic solutions and duality results for an abstract differential equation in HiIbert space are established. The dual variational method and a modification of the duality theory of Toland are used.
General
63
72
10.4171/ZAA/431
http://www.ems-ph.org/doi/10.4171/ZAA/431
Optimal Control of a Nonlinear Singular Integral Equation Arising in Electrochemical Machining
Manfred
Goebel
Universität Halle-Wittenberg, HALLE, GERMANY
Dieter
Oestreich
Hochschule für Technik und Wirtschaft Dresden, DRESDEN, GERMANY
The paper is concerned with an optimal control problem for a nonlinear singular integral equation of Cauchy type. The existence of at least one optimal solution is proved and a necessary optimality condition is derived.
General
73
82
10.4171/ZAA/432
http://www.ems-ph.org/doi/10.4171/ZAA/432
On an Iterative Algorithm for Solving Nonlinear Operator Equations
Ioannis
Argyros
Cameron University, LAWTON, UNITED STATES
Banach space, Secant method, Lipschitz-Hölder continuity
The Secant method for solving nonlinear operator equations in Banach spaces is considered. By assuming that the Fréchet derivative of a nonlinear operator is only Hölder continuous we show that the secant iteration converges to a locally unique solution. Examples are also given where our results apply and some related ones already in the literature fail.
Numerical analysis
83
92
10.4171/ZAA/433
http://www.ems-ph.org/doi/10.4171/ZAA/433
Quadrature Formula, FEM-Approximation (in Russian)
S.G.
Michlin
, ST. PETERSBURG, RUSSIAN FEDERATION
The author has constructed in one of his preceeding papers a FEM-approximation formula for functions of the class $C^{(s)} [0, 1]$ ($s$ an arbitrary natural number) which depends only on the values of the given function at the knots of the net. This construction demands to continue the given function (with preserving the class $C^{(s)}$ on a little segment of one or both sides of the segment [0, 1]. Accordingly one obtains two approximate formulae. Integrating them one obtains two quadrature formulae which accuracy depends from $s$. The right-hand side of every of them is the sum of the right-hand side of the classical trapezoid rule and some boundary layer. If one use bilateral continuation, then the boundary layer becomes a little more complicated, but the accuracy of the quadrature formula increases.
General
93
106
10.4171/ZAA/434
http://www.ems-ph.org/doi/10.4171/ZAA/434
On Imbeddings between Weighted Orlicz Spaces
Miroslav
Krbec
, PRAHA, CZECH REPUBLIC
Luboš
Pick
Charles University, PRAHA 8, CZECH REPUBLIC
Necessary and sufficient conditions are given for weight functions $\varrho$ and $\sigma$, which guarantee validity of the imbedding between the Orlicz spaces $L_{Q,\varrho} \hookrightarrow L_{P, \sigma}$. We make use of two methods: the first of them is a limit procedure leading to the imbedding of weighted Zygnwnd classes into weighted $L_1$, the second method employs the concept of duality in weighted Orlicz spaces, index of a Young function and results in a general imbedding theorem.
General
107
117
10.4171/ZAA/435
http://www.ems-ph.org/doi/10.4171/ZAA/435