Details

Autor(en) / Beteiligte

• Ferrera, J
• López-Gómez, Julián
• Ruiz del Portal, F. R

Titel

Ten mathematical essays on approximation in analysis and topology [electronic resource]

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and index.
• front cover; copyright; table of contents; front matter; Preface; body; Maximum Principles and Principal Eigenvalues; Introduction 1; Elliptic Boundary Value Problems; Notations and Conventions; Weak Maximum Principles; Nonhomogeneous Problems; The Principal Eigenvalue; The Strong Maximum Principle; Monotonicity of the Principal Eigenvalue; Continuity of the Principal Eigenvalue; Minimax Characterizations; Concavity of the Principal Eigenvalue; Preparatory Considerations; The Strong Maximum Principle for the Scalar Case; Strong and Weak Solutions; Resolvent Positivity
• Proofs of the Weak Maximum PrinciplesBounded Domains; Domain Perturbations; Elliptic Comparison Theorems; References 1; On Some Approximation Problems in Topology; Anti-Cech Approximation; Large Scale Topology (Large vs Small); Coarse Category; Cech and Anti-Cech Approximations; Geometry of Nerves; Property A; Coarse Approach to the Novikov Conjecture; Coarse Embeddings; Expanders; Polynomial Dimension Growth; Nonpositively Curved Manifolds; Mapping Intersection Problem; Cohomological Dimension; Extending Maps to CW Complexes; Negligibility Criterion; Reduction to other Approximation Problems
• The Codimension Three CaseReferences 2; Eigenvalues and Perturbed Domains; Introduction 3; Regular Domain Perturbations; Torsional Rigidity; Eigenvalues; Bifurcation and Generecity; Irregular Domains and Dirichlet Boundary Conditions; General Elliptic Operators; Operators in Divergence Form; Neumann Conditions and Irregular Perturbations; Perturbations near Boundary Points; Dumbbell Shaped Domains; Thin Domains; General Variations; References 3; Monotone Approximations and Rapid Convergence; Introduction 4; Successive Approximations; Personal Circumstances; Monotone Approximations
• Rapid ConvergenceReferences 4; Spectral Theory and Nonlinear Analysis; Introduction 5; General Assumptions and Basic Concepts; A Brief Introduction to the Topological Degree; Topological Characterization of Nonlinear Eigenvalues; Algebraic Characterizations of Nonlinear Eigenvalues; Global Behaviour of Compact Components; References 5; Approximating Topological Spaces by Polyhedra; Introduction 6; Properties Preserved under Inverse Limits; Spaces as Limits of Polyhedral Systems with Additional Properties; Resolutions of Spaces; Approximate Inverse Systems; Approximate Resolutions of Spaces
• Homotopy Expansions of SpacesReferences 6; Periodic Solutions in the Golden Sixties; Introduction 7; Weakly Nonlinear Systems; Cesari's Method for Strongly Nonlinear Systems; Topological Degree and Cronin's Monograph; Injecting Brouwer degree in Cesari's Method; Applying Leray-Schauder's Degree; Learning from History; References 7; The Stability of the Equilibrium; Introduction 8; Perpetual Stability and Discrete Dynamical Systems; The Linear Equation and the Symplectic Group; Degree Theory and Index of Zeros; The Index of an Equilibrium; Stability and Index; The Pendulum of Variable Length
• References 8
• This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces
• English