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Iterated function systems, moments, and transformations of infinite matrices / Palle E.T. Jorgensen, Keri A. Kornelson, Karen L. Shuman.

Author/Creator:
Jørgensen, Palle E. T., 1947- author.
Publication:
Providence, Rhode Island : American Mathematical Society, 2011.
Format/Description:
Book
1 online resource (105 p.)
Series:
Memoirs of the American Mathematical Society ; Number 1003.
Memoirs of the American Mathematical Society, 0065-9266 ; Number 1003
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Subjects:
Infinite matrices.
Transformations (Mathematics).
Iterative methods (Mathematics).
Form/Genre:
Electronic books.
Language:
English
Contents:
""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""
Notes:
"September 2011, volume 213, number 1003 (fourth of 5 numbers)."
Includes bibliographical references.
Description based on print version record.
Contributor:
Kornelson, Keri A., 1967- author.
Shuman, Karen L., 1973- author.
ISBN:
1-4704-0620-9