CHAPTER 1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs
1.Locally Convex Vector Spaces
2.Hahn-Banach Theorems
3.Dual Pairs
Notes and Remarks
CHAPTER 2 Radon Measures and Integral Representations
1.Introduction to Radon Measures on Hausdorff Spaces
2.The Riesz Representation Theorem
3.Weak Convergence of Finite Radon Measures
4.Vague Convergence of Radon Measures on Locally Compact Spaces
5.Introduction to the Theory of lntegral Representations
Notes and Remarks
CHAPTER 3 General Results on Positive and Negative Definite Matrices and Kernels
1.Definitions and Some Simple Properties of Positive and Negative Definite Kernels
2.Relations Between Positive and Negative Definite Kernels
3.Hilbert Space Representation of Positive and Negative Definite Kernels
Notes and Remarks
CHAPTER 4 Main Results on Positive and Negative Definite Functions on Semigroups
1.Definitions and Simple Properties
2.Exponentially Bounded Positive Definite Functions on Abelian Semigroups
3.Negative Definite Functions on Abelian Semigroups
4.Examples of Positive and Negative Defnite Functions
5.Positive Functions
6.Completely Monotone and Alternating Functions
Notes and Remarks
CHAPTER 5 Schoenberg-Type Results for Positive and Negative Definite Functions
1.Schoenberg Triples
2.Norm Dependent Positive Definite Functions on Banach Spaces
3.Functions Operating on Positive Definite Matrices
4.Schoenberg's Theorem for the Complex Hilbert Sphere
5.The Real Infinite Dimensional Hypcrbolic Space
Notes and Remarks
CHAPTER 6 Positive Definite Functions and Moment Functions
1.Moment Functions
2.The One-Dimensional Moment Problem
3.The Multi Dimensional Moment Problem
4.The Two-Sided Moment Problem
5.Perfect Semigroups
Notes and Remarks
CHAPTER 7 Hoeffding's Inequality and Multivariate Majorization
1.The Discrete Case
2.Extension to Nondiscrete Semigroups
3.Completely Negative Definite Functions and Schur-Monotonicity Notes and Remarks
CHAPTER 8 Positive and Negative Definite Functions on Abelian Semigroups Without Zero
1.Quasibounded Positive and Negative Definite Functions
2.Completely Monotone and Completely Alternating Functions
Notes and Remarks
References
List of Symbols
Index
