Korovkin-type Approximation Theory and Its Applications

Introduction\nInterdependence of sections\nNotation\nChapter 1. Preliminaries\n1.1 Topology and analysis\n1.2 Radon measures\n* 1.3 Some basic principles of probability theory\n1.4 Selected topics on locally convex spaces\n* 1.5 Integral representation theory for convex compact sets\n* 1.6 Co-Semigroups of operators and abstract Cauchy problems\nChapter 2. Korovkin-type theorems for bounded positive Radon measures\n2.1 Determining subspaces for bounded positive Radon measures\n2.2 Determining subspaces for discrete Radon measures\n2.3 Determining subspaces and Chebyshev systems\n2.4 Convergence subspaces associated with discrete Radon measures\n2.5 Determining subspaces for Dirac measures\n2.6 Choquet boundaries\nChapter 3. Korovkin-type theorems for positive linear operators\n3.1 Korovkin closures and Korovkin subspaces for positive linear operators\n3.2 Special properties of Korovkin closures\n3.3 Korovkin subspaces for positive projections\n3.4 Korovkin subspaces for finitely defined operators\nChapter 4. Korovkin-type theorems for the identity operator\n4.1 Korovkin closures and Korovkin subspaces for the identity operator\n4.2 Strict Korovkin subsets. Korovkin’s theorems\n4.3 Korovkin closures and state spaces. Spaces of parabola-like functions\n4.4 Korovkin closures and Stone-Weierstrass theorems\n4.5 Finite Korovkin sets\nChapter 5. Applications to positive approximation processes on real intervals\n5.1 Moduli of continuity and degree of approximation by positive linear operators\n5.2 Probabilistic methods and positive approximation processes\n5.3 Discrete-type approximation processes\n5.4 Convolution operators and summation processes\nChapter 6. Applications to positive approximation processes on convex compact sets\n6.1 Positive approximation processes associated with positive projections\n6.2 Positive projections and their associated Feller semigroups\n6.3 Miscellaneous examples and degenerate diffusion equations on convex compact subsets of ℝP\nAppendices\nA. Korovkin-type approximation theory on commutative Banach algebras\nA.1 Universal Korovkin-type approximation theory on commutative Banach algebras\nA.2 Commutative group algebras\nA.3 Finitely generated commutative Banach algebras and polydisk algebras\nA.4 Generalized analytic functions and algebras generated by inner functions\nA.5 Extreme spectral states and the Gleason-Kahane-Zelazko property\nB. Korovkin-type approximation theory on C*-algebras\nB.1 Approximation by positive linear functionals\nB.2 Approximation by positive linear operators\nC. A list of determining sets and Korovkin sets\nC.1 Determining sets in C0(X) (X locally compact Hausdorff space)\nC.2 Determining sets in C(X) (X compact)\nC.3 Korovkin sets in C0(X) (X locally compact Hausdorff space)\nC.4 Korovkin sets in C(X) (X compact Hausdorff space)\nC.5 Korovkin sets in Lp(Χ,μ)-spaces\nD. A subject classification of Korovkin-type approximation theory with a subject index\nD.1 Subject classification (SC)\nD.2 Subject index\nBibliography\nSymbol index\nSubject index