Korovkin-type Approximation Theory and Its Applications

Francesco Altomare, Michele Campiti

• Publisher: De Gruyter
• Year: 2011
• ISBN:
  9783110884586
• Edition: 1
• Topic: Matemáticas
• Subtopic: Matemáticas general

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Table of contents

• Introduction
• Interdependence of sections
• Notation
• Chapter 1. Preliminaries
• 1.1 Topology and analysis
• 1.2 Radon measures
• * 1.3 Some basic principles of probability theory
• 1.4 Selected topics on locally convex spaces
• * 1.5 Integral representation theory for convex compact sets
• * 1.6 Co-Semigroups of operators and abstract Cauchy problems
• Chapter 2. Korovkin-type theorems for bounded positive Radon measures
• 2.1 Determining subspaces for bounded positive Radon measures
• 2.2 Determining subspaces for discrete Radon measures
• 2.3 Determining subspaces and Chebyshev systems
• 2.4 Convergence subspaces associated with discrete Radon measures
• 2.5 Determining subspaces for Dirac measures
• 2.6 Choquet boundaries
• Chapter 3. Korovkin-type theorems for positive linear operators
• 3.1 Korovkin closures and Korovkin subspaces for positive linear operators
• 3.2 Special properties of Korovkin closures
• 3.3 Korovkin subspaces for positive projections
• 3.4 Korovkin subspaces for finitely defined operators
• Chapter 4. Korovkin-type theorems for the identity operator
• 4.1 Korovkin closures and Korovkin subspaces for the identity operator
• 4.2 Strict Korovkin subsets. Korovkin’s theorems
• 4.3 Korovkin closures and state spaces. Spaces of parabola-like functions
• 4.4 Korovkin closures and Stone-Weierstrass theorems
• 4.5 Finite Korovkin sets
• Chapter 5. Applications to positive approximation processes on real intervals
• 5.1 Moduli of continuity and degree of approximation by positive linear operators
• 5.2 Probabilistic methods and positive approximation processes
• 5.3 Discrete-type approximation processes
• 5.4 Convolution operators and summation processes
• Chapter 6. Applications to positive approximation processes on convex compact sets
• 6.1 Positive approximation processes associated with positive projections
• 6.2 Positive projections and their associated Feller semigroups
• 6.3 Miscellaneous examples and degenerate diffusion equations on convex compact subsets of ℝP
• Appendices
• A. Korovkin-type approximation theory on commutative Banach algebras
• A.1 Universal Korovkin-type approximation theory on commutative Banach algebras
• A.2 Commutative group algebras
• A.3 Finitely generated commutative Banach algebras and polydisk algebras
• A.4 Generalized analytic functions and algebras generated by inner functions
• A.5 Extreme spectral states and the Gleason-Kahane-Zelazko property
• B. Korovkin-type approximation theory on C*-algebras
• B.1 Approximation by positive linear functionals
• B.2 Approximation by positive linear operators
• C. A list of determining sets and Korovkin sets
• C.1 Determining sets in C0(X) (X locally compact Hausdorff space)
• C.2 Determining sets in C(X) (X compact)
• C.3 Korovkin sets in C0(X) (X locally compact Hausdorff space)
• C.4 Korovkin sets in C(X) (X compact Hausdorff space)
• C.5 Korovkin sets in Lp(Χ,μ)-spaces
• D. A subject classification of Korovkin-type approximation theory with a subject index
• D.1 Subject classification (SC)
• D.2 Subject index
• Bibliography
• Symbol index
• Subject index