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Positive definite functions on infinite-dimensional convex cones
About this Title
Helge Glöckner
Publication: Memoirs of the American Mathematical Society
Publication Year:
2003; Volume 166, Number 789
ISBNs: 978-0-8218-3256-1 (print); 978-1-4704-0387-4 (online)
DOI: https://doi.org/10.1090/memo/0789
MathSciNet review: 2008256
MSC: Primary 43A35; Secondary 43A65, 47A57, 47B65
Table of Contents
Chapters
- I. Preliminaries and preparatory results
- 1. Bounded and unbounded operators
- 2. Cone-valued measures
- 3. Measures on topological spaces
- 4. Projective limits of cone-valued measures
- 5. Holomorphic functions
- 6. Involutive semigroups and their representations
- 7. Positive definite kernels and functions
- 8. $C$*-algebras associated with involutive semigroups
- 9. Integral representations of positive definite functions
- 10. Convex cones and their faces
- 11. Examples of convex cones
- 12. Conelike semigroups: definition and examples
- 13. Representations of conelike semigroups I
- 14. Fourier and Laplace transforms
- 15. Generalized Bochner and Stone theorems
- II. Main results
- 16. Nussbaum Theorem for open convex cones
- 17. Positive definite functions on convex cones with non-empty interior
- 18. Positive definite functions on convex sets
- 19. Associated Hilbert spaces and representations
- 20. Nussbaum Theorem for generating convex cones
- 21. Representations of conelike semigroups II
- 22. Associated unitary representations
- 23. Holomorphic extension of unitary representations
- 24. Holomorphic extension of representations of nuclear groups