Vector and Operator Valued Measures and Applications
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Vector and Operator Valued Measures and Applications

  1. 474 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Vector and Operator Valued Measures and Applications

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About This Book

Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483261027
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Vector and Operator Valued Measures and Applications
  3. Copyright Page
  4. Table of Contents
  5. PARTCIPANTS
  6. PREFACE
  7. CHAPTER 1. SOME REMARKS ON A KOLMOGOV
  8. CHAPTER 2. ON EXPOSED POINTS OF THE RANGE
  9. CHAPTER 3. A SURVEY OF SOME RECENT RESULTS ON COMPACT MAPPINGS
  10. CHAPTER 4. A SUVEY OF DANIELL INTEGRATION
  11. CHAPTER 5. DANIELL AND DANIELL-BOCHNER TYPE INTEGRALS
  12. CHAPTER 6. EQUICONTINUITY, ABSOLUTE CONTINUITY AND WEAK COMACTNESS IN MEASURE THEORY
  13. CHAPTER 7. INDEPENDENCE AND CONTRACTIVE PROJECTIONS ON L ÎĄ
  14. CHAPTER 8. DISINTEGRATION OF MEASURES AND LIFTING
  15. CHAPTER 9. THE RADON-NIKODYM THEOREM FOR VECTOR MEASURES WITH VALUES IN THE DUALS OF S(M NUCLEAR SPACES
  16. CHAPTER 10. GROTHENDIBCK SPACES AND VECTOR MEASURES
  17. CHAPTER 11. LINEAR OPERATIONS ON Lp -SPACES
  18. CHAPTER 12. A NOTE ON PRODUCTS OF SPECTRAL MEASURES
  19. CHAPTER 13. VECTOR VALUED MEASURES AND DECOMPOSING MAPS
  20. CHAPTER 14. THE YOSIDA-HEWIIT DECOMPOSITION AS AN ERGODIC THEOREM
  21. CHAPTER 15. STOCHASTIC INTEGRATION
  22. CHAPTER 16. THE SPECTRAL INTEGRAL IN SCATTERING THEORY
  23. CHAPTER 17. PRE-MEASURES ON LATTICES OF SETS - II
  24. CHAPTER 18. ON THE BOCHNER INTEGRAL
  25. CHAPTER 19. THE EXTENSION AND CLOSURE OF VECTOR MEASURE
  26. CHAPTER 20. HIGHER-ORDER DIFFERENTIABILITY OF THE NORM IN Lp(E)
  27. CHAPTER 21. PERMANENCE PROPERTIES OF ABSOLUTE CONTINUITY CONDITIONS
  28. CHAPTER 22. ON THE STOJCTURE OF L2,Μ
  29. CHAPTER 23. RADON-NIKODYM THEORY FOR OPERATOR VALUED MEASURES AND A THEOREM OF FOURES & SEGAL
  30. CHAPTER 24. A GENERAL RADON-NIKODYM THEOREM
  31. CHAPTER 25. STOCHASTIC INTEGRATION
  32. CHAPTER 26. STOCHASTIC INTEGRAL AND VECTOR VALUED MEASURES
  33. CHAPTER 27. VECTOR-VALUED MEASURES RELATED TO A GENERALIZED CONTINUOUS HOMOGENEOUS RANDOM FIELD
  34. CHAPTER 28. RH4ARKS ON A RADON-NIKODYM THEORY FOR VECTOR MEASURES
  35. CHAPTER 29. CAUSAL FACTORIZATION, SHIFT OPERATORS AND THE SPECTRAL MULTIPLICITY FUNCTION
  36. CHAPTER 30. INTEGRAL AS A CERTAIN TYPE OF A POSITIVE DEFINITE FUNCTION
  37. CHAPTER 31. VECTOR MEASURES AND THE SPECTRAL THEOREM
  38. CHAPTER 32. L-ORTHOGONALLY SCATTERED MEASURES
  39. CHAPTER 33. ABSOLUTELY SIMIING OPERATORS ON CX(S)
  40. CHAPTER 34. S-BOUNDED ADDITIVE SET FUNCTIONS
  41. CHAPTER 35. SOME REMARKS ON THE NOTION OF "DERIVATIVES
  42. CHAPTER 36. A SURVEY OF MEAN CONVERGENCE OF MARTINGALES OF PETTIS INTEGRABLE FUNCTIONS
  43. CHAPTER ON THE CONSTRUCTION OF THE HILBERT SPACE L2,M FOR AN OPERATOR-VALUED MEASURE M
  44. BIBLIOGRAPHY