Approximation of Metric Spaces with Applications in Potential Theory
Author: Arnoldus Bernardus Jacobus Kuijlaars
Publisher:
Published: 1991
Total Pages: 103
ISBN-13:
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Linear Approximations in Convex Metric Spaces and the Application in the Mixture Theory of Probability Theory
Author: Bla Gyires
Publisher: World Scientific
Published: 1993
Total Pages: 148
ISBN-13: 9789810214838
DOWNLOAD EBOOKThis book focuses on the problem of linear approximability, or decomposability for distribution functions. While questions concerning this topics had been raised long ago, only ?ad hoc? procedures had been found out. Here, the author deals with the treatment of general methods for this problem.
Linear Approximations In Convex Metric Spaces And The Applicatn In The Mixture Theory Of Probability
Author: Bela Gyires
Publisher: World Scientific
Published: 1993-09-30
Total Pages: 141
ISBN-13: 9814502863
DOWNLOAD EBOOKThis book focuses on the problem of linear approximability, or decomposability for distribution functions. While questions concerning this topics had been raised long ago, only “ad hoc” procedures had been found out. Here, the author deals with the treatment of general methods for this problem.
Nonlinear Potential Theory on Metric Spaces
Author: Tero Mäkäläinen
Publisher:
Published: 2008
Total Pages: 98
ISBN-13: 9789513932695
DOWNLOAD EBOOKPotential Theory on Sierpiński Carpets
Author: Dimitrios Ntalampekos
Publisher: Springer Nature
Published: 2020-09-01
Total Pages: 186
ISBN-13: 3030508056
DOWNLOAD EBOOKThis self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpiński carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.
Recent Advances on Quasi-Metric Spaces
Author: Andreea Fulga
Publisher: MDPI
Published: 2020-06-03
Total Pages: 102
ISBN-13: 3039288814
DOWNLOAD EBOOKMetric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.
Nonlinear Potential Theory on Metric Spaces
Author: Anders Björn
Publisher: European Mathematical Society
Published: 2011
Total Pages: 422
ISBN-13: 9783037190999
DOWNLOAD EBOOKThe $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Approximation, Complex Analysis, and Potential Theory
Author: Norair Arakelian
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 275
ISBN-13: 9401009791
DOWNLOAD EBOOKHermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.
Exploring Mathematical Analysis, Approximation Theory, and Optimization
Author: Nicholas J. Daras
Publisher: Springer Nature
Published: 2024-01-04
Total Pages: 474
ISBN-13: 3031464877
DOWNLOAD EBOOKThis book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Approximation of Set-valued Functions
Author: Nira Dyn
Publisher:
Published: 2014
Total Pages: 153
ISBN-13: 9781783263028
DOWNLOAD EBOOKThis book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
