Geometry of moment spaces /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Karlin, Samuel, 1923-2007 (Autor), Shapely, Lloyd S., 1923- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 1953.
Colección:Memoirs of the American Mathematical Society ; no. 12.
Temas:
Moment spaces.
Espace-temps.
Moment spaces
Acceso en línea:Texto completo
Tabla de Contenidos:
  • CHAPTER I: CONVEX SETS
  • 1. Elementary definitions
  • 2. Boundary indices
  • 3. Convex representation
  • 4. Convex cones. Duality
  • 5. Conjugate points
  • CHAPTER II: THE MOMENT SPACE D[sup(n)] AND ITS DUAL P[sup(n)]
  • 6. Distribution functions on [0, 1]
  • 7. The moment space D[sup(n)]
  • 8. The polynomial space P[sup(n)]
  • 9. The boundary of P[sup(n)]
  • 10. A property of the extreme points of P[sup(n)]
  • 11. The boundary of D[sup(n)]
  • CHAPTER III: THE SIMPLEXES S[sup(n)] AND B[sup(n)]
  • 12. The simplex S[sup(n)]
  • 13. The dual simplex B[sup(n)]
  • 14. Fit of S[sup(n)] and B[sup(n)] to D[sup(n)] and P[sup(n)]
  • 15. Comparison of volumes
  • CHAPTER IV: ALGEBRAIC DESCRIPTION OF THE MOMENT SPACES
  • 16. Moment sequences and quadratic forms
  • 17. The determinants E[sub(m)] and their relation to the faces of D[sup(n)]
  • 18. The lower and upper boundaries of D[sup(n)]
  • CHAPTER V: DISTRIBUTIONS HAVING GIVEN MOMENTS
  • 19. The polynomials E[sub(m)](t) and E[sub(m)(t)
  • 20. Construction of distribution functions
  • 21. Characterization of the set of distribution functions with given moments
  • 22. Intertwining property of functions in D.
  • CHAPTER VI: APPLICATION TO ORTHOGONAL POLYNOMIALS
  • 23. Orthogonality of the E-polynomials
  • 24. Separation of roots. Christoffel numbers
  • 25. Geometry of the Tchebycheff polynomials
  • CHAPTER VII: SYMMETRIES OF THE MOMENT SPACES
  • 26. Reversal of the unit interval
  • 27. Moment space of symmetric distributions
  • 28. Other symmetries
  • REFERENCES.

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