- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 21:06:31
10
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=13&iss=2&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)
13
1994
2
On the Nakano Individual Convergence
R.
Zaharopol
Binghamton University, BINGHAMTON, UNITED STATES
Archimedean Riesz spaces, Dedekind completion, projection bands, Nakano individual convergence
We have recently defined the notion of individual convergence for a sequence of positive elements of an Archimedean Riesz space $E$. In the note we complete the definition (i.e., we define the individual convergence for sequences of not necessarily positive elements of $E$), and we prove that our notion of individual convergence is a natural extension of the individual convergence as defined by Nakano: we will prove that if a sequence of elements of $E$ has an individual limit in the Nakano sense, then it converges individually with respect to our definition.
Functional analysis
Operator theory
General
181
189
10.4171/ZAA/517
http://www.ems-ph.org/doi/10.4171/ZAA/517
On Stationary Incompressible Norton Fluids and some Extensions of Korn’s Inequality
Martin
Fuchs
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
Non-Newtonian fluids, Korn’s inequality
A simple mathematical model for a so-called Norton fluid is given. We study a variational problem and make use of appropriate versions of Korn’s inequality.
Calculus of variations and optimal control; optimization
Fluid mechanics
General
191
197
10.4171/ZAA/516
http://www.ems-ph.org/doi/10.4171/ZAA/516
Perron’s Method and Barrier Functions for the Viscosity Solutions of the Dirichlet Problem for some Non-Linear Partial Differential Equations
M.
Ramaswamy
Indian Institute of Science, BANGALORE, INDIA
S.
Ramaswamy
Indian Institute of Science, BANGALORE, INDIA
Viscosity super- and subsolutions, Perron families, resolutive functions, barriers
The Dirichlet problem for some non-linear partial differential equations via Perron’s method is studied in the viscosity set up, by considering two families of functions, instead of one, as considered by others before. The notion of barrier at a boundary point is introduced to study the regularity of boundary points. Barriers for some non-linear operators are also constructed.
Partial differential equations
General
199
207
10.4171/ZAA/515
http://www.ems-ph.org/doi/10.4171/ZAA/515
Asymptotic Formulas for Small Sessile Drops
Erich
Miersemann
Universität Leipzig, LEIPZIG, GERMANY
Capillarity, drops, asymptotic expansions
We will prove asymptotic foriiulas for the wetted disk of a drop with small volume resting on a horizontal plane which is in a vertical gravity field. These formulas are general-izations of results of Finn. There is a non-uniformity in the asymptotic behaviour depending on whether the boundary contact angle is near $\pi$ or not. If the contact angle is different from $\pi$ we get a complete asymptotic expansion of the wetted disk in powers of the volume. These results are consequences of the strong non-linearity of the problem.
Fluid mechanics
Partial differential equations
Approximations and expansions
General
209
231
10.4171/ZAA/514
http://www.ems-ph.org/doi/10.4171/ZAA/514
A Schur Type Analysis of the Minimal Unitary Hubert Space Extensions of a Krein Space Isometry whose Defect Subspaces are Hubert Spaces
Aad
Dijksma
Rijksuniversiteit Groningen, GRONINGEN, NETHERLANDS
S.A.M.
Marcantognini
Universidad Simón Bolívar, CARACAS, VENEZUELA
H.S.V.
de Snoo
Rijksuniversiteit Groningen, GRONINGEN, NETHERLANDS
Isometrics, unitary extensions, Krein spaces, Schur parameters, commutant lifting
We consider a Krein space isometry whose defect subspaces are Hilbert spaces and we show that its minimal unitary Hilbert space extensions are related to one-step isometric Hilbert space extensions and Schur parameters. These unitary extensions give rise to moments and scattering matrices defined on a scale subspace. By means of these notions we solve the labeling problem for the contractive intertwining liftings in the commutant lifting theorem for Krein space contractions.
Operator theory
General
233
260
10.4171/ZAA/513
http://www.ems-ph.org/doi/10.4171/ZAA/513
Spectral Estimates for Compact Hyperbolic Space Forms and the Selberg Zeta Function for $p$-Spectra II
Reinhard
Schuster
Universität Leipzig, LEIPZIG, GERMANY
Eigenvolue spectrum, Laplace operator, hyperbolic space form, length spectrum, Selberg zeta function, analytic number theory techniques
We prove an asymptotic estimation for the spectrum of the Laplace operator for compact hyperbolic space forms. Thereby we use estimations of the Selberg zeta function by methods of analytic number theory.
Number theory
Partial differential equations
Global analysis, analysis on manifolds
General
261
305
10.4171/ZAA/512
http://www.ems-ph.org/doi/10.4171/ZAA/512
On the Existence of Holomorphic Functions Having Prescribed Asymptotic Expansions
M.
Valdivia
Universidad de Valencia, BURJASOT (VALENCIA), SPAIN
Jean
Schmets
Sart Tilmann - BAT. B 37, LIÈGE 1, BELGIUM
Holomorphic functions, asymptotic expansions
A generalization of some results of T. Carleman in [1] is developped. The practical form of it states that if the non-empty subset $D$ of the boundary $\partial \Omega$ of a domain $\Omega$ of $C$ has no accumulation point and if the connected component in $\partial \Omega$ of every is $u \in D$ has more than one point, then $D$ is regularly asymptotic for $\Omega$, i.e. for every family {$c_{u,n}: u \in D, n \in \mathbb N_0$} of complex numbers, there is a holomorphic function $f$ on $\Omega$ which at every $u \in D$ has $\sum^{\infty}_{n=0} c_{u,n} (z–u)^n$ as asymptotic expansion at $u$.
Functions of a complex variable
Functional analysis
General
307
327
10.4171/ZAA/511
http://www.ems-ph.org/doi/10.4171/ZAA/511
Spline Approximation Methods Cutting Off Singularities
Steffen
Roch
Technische Hochschule Darmstadt, DARMSTADT, GERMANY
Spline approximation methods, singular integral operators, Mellin operators
The topic of this paper is some types of singular behavior of spline approximation methods for one-dimensional singular integral operators which are caused by discontinuities in the coefficients or by non-smooth geometries of the underlying curves. These singularities can be cutted off by a modification of the approximation method which is closely related to the finite or infinite section method for discrete Toeplitz operators. Using Banach algebra techniques, one can derive stability criteria for a large variety of modified methods (including Galerkin, collocation, and qualocation.
Numerical analysis
Operator theory
General
329
345
10.4171/ZAA/510
http://www.ems-ph.org/doi/10.4171/ZAA/510
On the Oscillatory Behaviour of Solutions of Second Order Nonlinear Difference Equations
E.
Thandapani
University of Madras, CHENNAI, INDIA
S.
Pandian
Periyar University, SALEM, INDIA
Second order nonlinear difference equations, oscillation
By using simple discrete inqualities sufficient conditions are provided for the solution {$y_n$} of a difference equation of the form $\Delta(a_n \Delta y_n) + q_{n+1} f (y_{n+1} = r_n (n \in \mathbb N_0; {a_n}, {q_n}, {r_n} C \mathbb R; f : \mathbb R \to \mathbb R)$ to be oscillatory or to satisfy lim inf$_{n \to \infty} |y_n| = 0$. Also two other results are established for all solutions of this equation to be oscillatory when $r_n = 0$ for all $n \in \mathbb N_0$.
Difference and functional equations
General
347
358
10.4171/ZAA/509
http://www.ems-ph.org/doi/10.4171/ZAA/509
On a Representation of the General Solution of a Functional-Differential Equation
M.
Drakhlin
College of Judea and Samaria, ARIEL, ISRAEL
E.
Litsyn
Bar-Ilan University, RAMAT GAN, ISRAEL
Functional-differential equations, superposition operators, Volterra operators
The general solution of a functional-differential equation with non-Volterra operator is found by its reducing to an infinite system. An integral representation of the general solution of this system is presented. Properties of the kernel of this system are studied.
Ordinary differential equations
Operator theory
General
359
364
10.4171/ZAA/508
http://www.ems-ph.org/doi/10.4171/ZAA/508