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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: http://dx.doi.org/10.1090/memo/0789
MathSciNet review: 2008256
MSC (2000): Primary 43A35; Secondary 43A65, 47A57, 47B65

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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. *-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