Author | Berg, Christian. author |
---|---|
Title | Harmonic Analysis on Semigroups [electronic resource] : Theory of Positive Definite and Related Functions / by Christian Berg, Jens Peter Reus Christensen, Paul Ressel |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1128-0 |
Descript | X, 292 p. online resource |
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs -- ยง1. Locally Convex Vector Spaces -- ยง2. Hahn-Banach Theorems -- ยง3. Dual Pairs -- Notes and Remarks -- 2 Radon Measures and Integral Representations -- ยง1. Introduction to Radon Measures on Hausdorff Spaces -- ยง2. The Riesz Representation Theorem -- ยง3. Weak Convergence of Finite Radon Measures -- ยง4. Vague Convergence of Radon Measures on Locally Compact Spaces -- ยง5. Introduction to the Theory of Integral Representations -- Notes and Remarks -- 3 General Results on Positive and Negative Definite Matrices and Kernels -- ยง1. Definitions and Some Simple Properties of Positive and Negative Definite Kernels -- ยง2. Relations Between Positive and Negative Definite Kernels -- ยง3. Hubert Space Representation of Positive and Negative Definite Kernels -- Notes and Remarks -- 4 Main Results on Positive and Negative Definite Functions on Semigroups -- ยง1. Definitions and Simple Properties 86 ยง2. Exponentially Bounded Positive Definite Functions on Abelian Semigroups -- ยง3. Negative Definite Functions on Abelian Semigroups -- ยง4. Examples of Positive and Negative Definite Functions -- ยง5. T-Positive Functions -- ยง6. Completely Monotone and Alternating Functions -- Notes and Remarks -- 5 Schoenberg-Type Results for Positive and Negative Definite Functions -- ยง1. Schoenberg Triples -- ยง2. Norm Dependent Positive Definite Functions on Banach Spaces -- ยง3. Functions Operating on Positive Definite Matrices -- ยง4. Schoenbergโs Theorem for the Complex Hilbert Sphere -- ยง5. The Real Infinite Dimensional Hyperbolic Space -- Notes and Remarks -- 6 Positive Definite Functions and Moment Functions -- ยง1. Moment Functions -- ยง2. The One-Dimensional Moment Problem -- ยง3. The Multi-Dimensional Moment Problem -- ยง4. The Two-Sided Moment Problem -- ยง5. Perfect Semigroups -- Notes and Remarks -- 7 Hoeffdingโs Inequality and Multivariate Majorization -- ยง1. The Discrete Case -- ยง2. Extension to Nondiscrete Semigroups -- ยง3. Completely Negative Definite Functions and Schur-Monotonicity -- Notes and Remarks -- 8 Positive and Negative Definite Functions on Abelian Semigroups Without Zero -- ยง1. Quasibounded Positive and Negative Definite Functions -- ยง2. Completely Monotone and Completely Alternating Functions -- Notes and Remarks -- References -- List of Symbols