03825nam 2200625 450 991048011600332120170822144504.01-4704-0620-9(CKB)3360000000465187(EBL)3114273(SSID)ssj0000889016(PQKBManifestationID)11453163(PQKBTitleCode)TC0000889016(PQKBWorkID)10876002(PQKB)11488566(MiAaPQ)EBC3114273(PPN)195418921(EXLCZ)99336000000046518720150417h20112011 uy 0engur|n|---|||||txtccrIterated function systems, moments, and transformations of infinite matrices /Palle E.T. Jorgensen, Keri A. Kornelson, Karen L. ShumanProvidence, Rhode Island :American Mathematical Society,2011.©20111 online resource (105 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 1003"September 2011, volume 213, number 1003 (fourth of 5 numbers)."0-8218-5248-5 Includes bibliographical references.""Contents""; ""Preface""; ""Chapter 1. Notation""; ""1.1. Hilbert space notation""; ""1.2. Unbounded operators""; ""1.3. Multi-index notation""; ""1.4. Moments and moment matrices""; ""1.5. Computations with infinite matrices""; ""1.6. Inverses of infinite matrices""; ""Chapter 2. The moment problem""; ""2.1. The moment problem M = M()""; ""2.2. A Parthasarathy-Kolmogorov approach to the moment problem""; ""2.3. Examples""; ""2.4. Historical notes""; ""Chapter 3. A transformation of moment matrices: the affine case""; ""3.1. Affine maps""""3.2. IFSs and fixed points of the Hutchinson operator""""3.3. Preserving Hankel matrix structure""; ""Chapter 4. Moment matrix transformation: measurable maps""; ""4.1. Encoding matrix A for ""; ""4.2. Approximation of A with finite matrices""; ""Chapter 5. The Kato-Friedrichs operator""; ""5.1. The quadratic form QM""; ""5.2. The closability of QM""; ""5.3. A factorization of the Kato-Friedrichs operator""; ""5.4. Kato connection to A matrix""; ""5.5. Examples""; ""Chapter 6. The integral operator of a moment matrix""; ""6.1. The Hilbert matrix""""6.2. Integral operator for a measure supported on [-1,1]""""Chapter 7. Boundedness and spectral properties""; ""7.1. Bounded Kato operators""; ""7.2. Projection-valued measures""; ""7.3. Spectrum of the Kato operator""; ""7.4. Rank of measures""; ""7.5. Examples""; ""Chapter 8. The moment problem revisited""; ""8.1. The shift operator and three incarnations of symmetry""; ""8.2. Self-adjoint extensions of a shift operator""; ""8.3. Self-adjoint extensions and the moment problem""; ""8.4. Jacobi representations of matrices""""8.5. The triple recursion relation and extensions to higher dimensions""""8.6. Concrete Jacobi matrices""; ""Acknowledgements""; ""Bibliography""Memoirs of the American Mathematical Society ;Number 1003.Infinite matricesTransformations (Mathematics)Iterative methods (Mathematics)Electronic books.Infinite matrices.Transformations (Mathematics)Iterative methods (Mathematics)512.9/434 Jørgensen Palle E. T.1947-862064Kornelson Keri A.1967-Shuman Karen L.1973-MiAaPQMiAaPQMiAaPQBOOK9910480116003321Iterated function systems, moments, and transformations of infinite matrices2175547UNINA