| Description |
1 online resource (101 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 12 |
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Memoirs of the American Mathematical Society ; no. 12.
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| Contents |
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)] |
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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 |
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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 |
| Bibliography |
Includes bibliographical references (pages 92-93) |
| Notes |
Print version record |
| Subject |
Moment spaces.
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Moment spaces.
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| Form |
Electronic book
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| Author |
Shapely, Lloyd S., 1923- author
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| ISBN |
9780821899175 |
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0821899171 |
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