- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 20:27:49
15
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=12&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)
12
1993
2
Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems
Peter
Massopust
Vanderbilt University, NASHVILLE, UNITED STATES
Iterated function systems, fractal functions and surfaces, attractors, box dimensions
We construct $C^1$- and $C^2$-interpolating fractal functions using a certain class of iterated function systems. An estimate for the box dimension of the graph of nonsmooth fractal functions generated by this new class is presented. We then generalize this construction to hi variate functions thus obtaining $C^1$-interpolating fractal surfaces. Finally, $C^n$-interpolating fractal surfaces are constructed via integration over $C^0$ fractal surfaces.
Real functions
Approximations and expansions
Global analysis, analysis on manifolds
201
210
10.4171/ZAA/571
http://www.ems-ph.org/doi/10.4171/ZAA/571
Two-Sided Nevanlinna-Pick Interpolation for a Class of Matrix-Valued Functions
Daniel
Alpay
Ben Gurion University of the Negev, BEER SHEVA, ISRAEL
Vladimir
Bolotnikov
College of William and Mary, WILLIAMSBURG, UNITED STATES
Nevanlinna-Pick interpolation, reproducing kernel spaces, fundamental matrix inequalities
Families of Matrix-valued analytic functions $W(\rho, P)$ depending on two parameters $\rho$ and $P$ are introduced. These include as special cases the Schur and Carathéodory functions, as well as classes of functions studied by the authors in [1] and by D. Alpay and H. Dym in [6]. A two sided Nevanlinna-Pick interpolation problem is defined and solved in $W(\rho, P)$, using the fundamental matrix inequality method.
Operator theory
Functions of a complex variable
211
238
10.4171/ZAA/570
http://www.ems-ph.org/doi/10.4171/ZAA/570
On the Weyl Matrix Balls Associated with Nondegenerate Matrix-Valued Carathéodory Functions
B.
Fritzsche
Universität Leipzig, LEIPZIG, GERMANY
B.
Kirstein
Universität Leipzig, LEIPZIG, GERMANY
Matrix-valued Carathéodory functions, Weyl matrix balls, limit behaviour of the semi-radii
The paper is aimed at a study of the limit behaviour of the normalized semi-radii of the Weyl matrix balls associated with a nondegenerate matrix-valued Carathodory function. It turns out that the ranks of the limits of these normalized semi-radii are constant within the unit disc. This enables us a new classification of matrix-valued Carathéodory functions.
Functions of a complex variable
239
261
10.4171/ZAA/569
http://www.ems-ph.org/doi/10.4171/ZAA/569
Interdependent Components of Generating Systems in the Theory of Pseudo-Holomorphic Functions
C.
Withalm
Karl-Franzens-Universität Graz, GRAZ, AUSTRIA
pseudo-holomorphic functions, distinctive generating systems, singularities
In many studies concerning the theory of pseudo-holomorphic functions in the sense of L. Bers the interdependence of the components of a relevant generating system turns out to be essential to investigate, e.g. inquiring into periodicity problems with respect to corresponding derivatives but also into multiple reasonable configurations.
Functions of a complex variable
Partial differential equations
263
272
10.4171/ZAA/568
http://www.ems-ph.org/doi/10.4171/ZAA/568
On Transformations of Distribution Functions on the Unit Interval - a Generalization of the Gauß-Kuzmin-Lévy Theorem
Peter
Schatte
Bergakademie Freiberg, FREIBERG, GERMANY
Piecewise monotonic transformations, Frobenius-Perron operators, invariant measures, uniform distribution of sequences, metric theory of continued fractions
Global analysis, analysis on manifolds
Number theory
Measure and integration
273
283
10.4171/ZAA/567
http://www.ems-ph.org/doi/10.4171/ZAA/567
Eigenva1ue Distribution of Invariant Linear Second Order Elliptic Differential Operators with Constant Coefficients
M.
Belger
Universität Leipzig, LEIPZIG, GERMANY
Eigenvalue problem, eigenvalue distribution, invariant linear elliptic differential operator, lattice remainder, asymptotic estimation principal vector
Operator theory
Partial differential equations
285
296
10.4171/ZAA/566
http://www.ems-ph.org/doi/10.4171/ZAA/566
Axially Symmetric Flow with Finite Cavities II
Friedemann
Brock
Universität Leipzig, LEIPZIG, GERMANY
Non-continuous functional, symmetrization, axially symmetric flow
An axially symmetric cavity flow of an ideal fluid is moving around an obstacle. The flow is either in a cylindrical pipe or an unbounded region and the cavity may be finite. Essentially is the assumption that the obstacle is star-like with respect to some point on the axis of symmetry. The existence of such flows was proved by the author in Part I. In the present Part lithe behaviour of the free boundaries near the end-point on the axis of symmetry (in the case of a finite cavity) and near infinity (in the case of an infinite cavity) are investigated.
Partial differential equations
297
303
10.4171/ZAA/565
http://www.ems-ph.org/doi/10.4171/ZAA/565
The Smoothness of the Solution to a Two-Dimensional Integral Equation with Logarithmic Kernel
U.
Kangro
Carnegie Mellon University, PITTSBURGH, UNITED STATES
Weakly singular integral equations, smoothness of the solution
We observe a two-dimensional weakly singular integral equation with logarithmic kernel. The behavior of the higher order derivatives of the solution to the equation is examined in case of bounded domain of Integration with piecewise smooth boundary. Exact descriptions for the leading terms of the derivatives and estimations for the remainders are given.
Integral equations
305
318
10.4171/ZAA/564
http://www.ems-ph.org/doi/10.4171/ZAA/564
On the Solution of an Ill-Posed Non-Linear Fredholm Integral Equation Connected with an Inverse Problem of Thin Film Optics
H.
Schachtzabel
Universität Potsdam, POTSDAM, GERMANY
H.-A.
Braunss
Universität Potsdam, POTSDAM, GERMANY
B.
Hofmann
Technische Hochschule, ZITTAU, GERMANY
Non-linear integral equations, optics
We carry out a theoretical analysis of the simultaneous identification of geometrical thick-ness and refractive index profile for inhomogeneous single layer systems from indirect mea-surements. The problem leads to a non-linear integral equation of the first kind with smooth kernel. We present a uniqueness theorem for monotone solutions referring to the Hausdorff moment problem.
Ordinary differential equations
Integral equations
Optics, electromagnetic theory
319
326
10.4171/ZAA/563
http://www.ems-ph.org/doi/10.4171/ZAA/563
Identifiability of the Transmissivity Coefficient in an Elliptic Boundary Value Problem
Gennadi
Vainikko
Tartu University, TARTU, ESTONIA
Karl
Kunisch
Karl-Franzens-Universität Graz, GRAZ, AUSTRIA
Inverse problems, ground water filtration problems, identifiability
We deal with a coefficient inverse problem describing the filtration of ground water in a region $\Omega \subset R^n, n ≥ 2$. Introducing a weak formulation of the problem, discretization and regularization methods can be constructed in a natural way. These methods converge to the normal solution of the problem, i.e. to a transmissivity coefficient of a minimal $L^2 (\Omega)$-norm. Thus a question about $L^2$-identifiability (identifiability among functions of the class $L^2 (\Omega)$ of the transmissivity coefficient arises. Our purpose is to describe subregions of $\Omega$ where the transmissivity coefficient is really $L^2$-identifiable or even $L^1$-identifiable. Thereby we succeed introducing physically realistic conditions on the data of the problem, e.g. piecewise smooth surfaces in $\Omega$ are allowed where the data of the inverse problem may have discontinuities. With some natural changes, our results about the $L^1$-identifiability extend known results about the identifiability among more smooth functions given by G. R. Richter [4], C. Chicone and J. Gerlach [1], and K. Kunisch [3].
Partial differential equations
Numerical analysis
327
341
10.4171/ZAA/562
http://www.ems-ph.org/doi/10.4171/ZAA/562
Integral and Boundary Value Problems for Nonlinear Systems of Composite Type
Leroy
Lundin
University of Delaware, NEWARK, UNITED STATES
Guochun
Wen
Peking University, BEIJING, CHINA
Nonlinear composite systems, Schauders fixed point theorem, a priori estimates
Using the Schauder fixed point theorem we establish the solvability of an initial-boundary va-lue problem for a nonlinear first order system of composite type. The procedure depends on first establishing a priori estimates for the solutions. This investigation generalizes the results of [1,3,4].
Partial differential equations
343
352
10.4171/ZAA/561
http://www.ems-ph.org/doi/10.4171/ZAA/561
On Approximation-Solvability of Nonlinear Equations in Reflexive Banach Spaces
Ram
Verma
University of Central Florida, ORLANDO, UNITED STATES
L.
Debnath
University of Central Florida, ORLANDO, UNITED STATES
Approximation scheme, approximation-solvability, $A$-proper mappings
We extend the Zarantonello numerical range to the case of reflexive Banach space opera-tors, and study the approximation-solvability of nonlinear equations relating to the results of Zeidler (1990).
Numerical analysis
353
360
10.4171/ZAA/560
http://www.ems-ph.org/doi/10.4171/ZAA/560
About Integral Equivalence between Linear and Nonlinear Operator Impulsive Differential Equations in a Banach Space
S.I.
Kostadinov
University of Plovdiv, PLOVDIV, BULGARIA
Dieter
Schott
Hochschule Wismar, WISMAR, GERMANY
Abstract impulsive differential equations, integral equivalence, asymptotic equivalence, exponential dichotomy, fixed point theorem of Schauder
After an introduction into the problems of impulsive operator differential equations sufficient conditions for the integral and the asymptotic equivalence between linear and nonlinear equations of this kind are presented. These conditions guarantee that for bounded solutions of the linear equation there are also bounded solutions of the corresponding nonlinear equation.
Ordinary differential equations
Operator theory
361
378
10.4171/ZAA/559
http://www.ems-ph.org/doi/10.4171/ZAA/559
The Optimal Runner: a Control Problem with Phase Constraint
C.
Hamburger
Universität Bonn, BONN, GERMANY
running, race, optimal velocity, phase constraint, mazimum principle
Assuming a simple biophysical model and using the Pontryagin maximum principle, we find the optimal strategy to run a race.
Calculus of variations and optimal control; optimization
379
391
10.4171/ZAA/558
http://www.ems-ph.org/doi/10.4171/ZAA/558
Observations on the preceding paper of C. Hamburger: The Optimal Runner: a Control Problem with Phase Constraint
L.
Pickenhain
, LEIPZIG, GERMANY
Assuming a simple biophysical model and using the Pontryagin maximum principle, we find the optimal strategy to run a race.
Calculus of variations and optimal control; optimization
393
393
10.4171/ZAA/557
http://www.ems-ph.org/doi/10.4171/ZAA/557