Harmonic Analysis of Probability Measures on Hypergroups
eBook - PDF

Harmonic Analysis of Probability Measures on Hypergroups

  1. 608 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Harmonic Analysis of Probability Measures on Hypergroups

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Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110121056
eBook ISBN
9783110877595
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Introduction
  2. 1 Hypergroups and their measure algebras
  3. 1.1 Definition and general constructions
  4. 1.2 Translation and convolution
  5. 1.3 Invariant measures
  6. 1.4 Convolution of functions
  7. 1.5 Subhypergroups and double coset hypergroups
  8. 1.6 Idempotent measures and multipliers
  9. Notes
  10. 2 The dual of a commutative hypergroup
  11. 2.1 Representations and Fourier transforms
  12. 2.2 The dual space in the commutative case
  13. 2.3 Modification of the convolution
  14. 2.4 The dual hypergroup
  15. 2.5 Support of the Plancherel measure
  16. Notes
  17. 3 Some special classes of hypergroups
  18. 3.1 Polynomial hypergroups in several variables
  19. 3.2 Polynomial hypergroups in one variable
  20. 3.3 Examples of polynomial hypergroups in one variable
  21. 3.4 One-dimensional hypergroups
  22. 3.5 Sturm-Liouville hypergroups
  23. 3.6 Characterization of Pontryagin hypergroups
  24. Notes
  25. 4 Positive and negative definite functions and measures
  26. 4.1 Positive definite functions
  27. 4.2 The Lévy continuity theorem
  28. 4.3 Positive definite measures
  29. 4.4 Negative definite functions
  30. 4.5 The Lévy-Khintchine representation
  31. Notes
  32. 5 Convolution semigroups and divisibility of measures
  33. 5.1 Convergence of nets of measures
  34. 5.2 Convolution semigroups of measures
  35. 5.3 Embedding infinitely divisible measures
  36. 5.4 Factorization on hermitian hypergroups
  37. Notes
  38. 6 Transience of convolution semigroups
  39. 6.1 The dichotomy theorem for random walks
  40. 6.2 The generalized Chung-Fuchs criterion
  41. 6.3 Transience and renewal of convolution semigroups
  42. 6.4 Characterization of potential measures
  43. 6.5 Invariant Dirichlet forms
  44. Notes
  45. 7 Randomized sums of hypergroup-valued random variables
  46. 7.1 Concretization of hypergroups
  47. 7.2 Moment functions
  48. 7.3 Strong laws of large numbers
  49. 7.4 Central limit theorems
  50. 7.5 Invariance principles
  51. Notes
  52. 8 Further topics
  53. 8.1 Towards a structure theory for hypergroups
  54. 8.2 Towards a theory of stationary random fields over hypergroups
  55. Bibliography
  56. Examples
  57. Symbols
  58. Index

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Yes, you can access Harmonic Analysis of Probability Measures on Hypergroups by Walter R. Bloom,Herbert Heyer in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over 1.5 million books available in our catalogue for you to explore.