03160nam 2200529 450 991047992920332120170821170811.00-8218-9917-1(CKB)3360000000463971(EBL)3113706(SSID)ssj0000973594(PQKBManifestationID)11594938(PQKBTitleCode)TC0000973594(PQKBWorkID)10984482(PQKB)10201185(MiAaPQ)EBC3113706(PPN)195408950(EXLCZ)99336000000046397120750507d1953 uy| 0engur|n|---|||||txtccrGeometry of moment spaces /by S. Karlin and L.S. ShapelyProvidence :American Mathematical Society,1953.1 online resource (101 p.)Memoirs of the American Mathematical Society ;number 12Description based upon print version of record.0-8218-1212-2 References: pages 92-93.""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)]""""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 Î?[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 Î?[sub(m)](t) and Î?[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|x""; ""CHAPTER VI: APPLICATION TO ORTHOGONAL POLYNOMIALS""; ""23. Orthogonality of the Î?-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""Memoirs of the American Mathematical Society ;no. 12.Moment spacesElectronic books.Moment spaces.Karlin Samuel1923-2007,3477Shapely Lloyd S.1923-MiAaPQMiAaPQMiAaPQBOOK9910479929203321Geometry of moment spaces2099186UNINA