Iterated Function Systems, Moments, and Transformations of Infinite Matrices.

Intro -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.