Interpolation, Schur Functions and Moment Problems II

Name: Interpolation, Schur Functions and Moment Problems II
Brand: Birkhäuser
Price: 53.49 EUR
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Daniel Alpay Bernd Kirstein(Herausgeber*in)

Birkhäuser (Verlag)

Erschienen am 25. Juli 2012

VI, 302 Seiten

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978-3-0348-0428-8 (ISBN)

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Intro
Interpolation, Schur Functions and Moment Problems II
Contents
Editorial Introduction
References
On the Concept of Invertibility for Sequences of Complex p × q-matrices and its Application to Holomorphic p × q-matrix-valued Functions
0. Introduction
1. Some notation
2. A first look at invertible sequences in Cp×q
3. The arithmetic of invertible sequences
4. Constructing the inverse sequence
5. A closer look at the set Dp×q,? and reciprocal sequences
6. Further observations on invertible sequences
7. Some considerations on EP sequences
8. Moore-Penrose pseudoinverses of holomorphic matrix-malued functions
Appendix A. The Moore-Penrose inverse of a complex matrix
References
On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions
0. Introduction
1. Reciprocal sequences
2. Matricial Toeplitz non-negative definite sequences
3. Matricial Carathéodory sequences
4. Reciprocal sequences of matricial Carathéodory sequences
5. Matricial Toeplitz non-negative definite sequences generated by reciprocation
6. Matricial Carathéodory functions
7. Moore-Penrose Inverses of Matricial Carathéodory Functions
8. An approach to constructing the reciprocal of a non-negative Hermitian q × q measure
9. Matricial R-functions in the open upper half-plane
Appendix A. Some facts from matrix theory
Acknowledgement
References
On a Schur-type Algorithm for Sequences of Complex p × q-matrices and its Interrelations with the Canonical Hankel Parametrization
1. Introduction
2. The canonical Hankel parametrization of sequences of p × q-Matrices
3. Some observations on finite and infinite sequences of matrices with particular Hankel-properties
4. Reciprocal sequences
5. Some identities for block Hankel matrices associated with Cauchy products
6. Some identities for block Hankel matrices formed by a sequence and its reciprocal
7.The shortened negative reciprocal sequence corresponding to a sequence from Dp ×q,?
8. The first Schur transform of a sequence of p × q-matrices
9. A Schur-type algorithm for sequences of complex p x q-matrices
10. Recovering the original sequence from the first Schur transform and first two matrices
Appendix A. The Moore-Penrose inverse of a complex matrix
Appendix B. On two particular multiplicative groups of triangular block matrices
References
Multiplicative Structure of the Resolvent Matrix for the Truncated Hausdorff Matrix Moment Problem
1. Introduction
2. Notation and preliminaries
2.1. Hausdorff matrix moment problem and the resolvent matrix
2.2. The resolvent matrix of the HMM problem
3. Main algebraic identities
4. The Blaschke-Potapov factors
Appendix A. Blaschke-Potapov representation of the resolvent matrix, the case of an even number of moments
Acknowledgment
References
On a Special Parametrization of Matricial a-Stieltjes One-sided Non-negative Definite Sequences
1. Introduction
2. Some facts on the classes of a-Stieltjes one-sided non-negative definite sequences and some of its subclasses
3. Canonical Hankel parametrization
4. One-sided a-Stieltjes parametrizations
5. Completely degenerate a-Stieltjes non-negative definite sequences
6. Connection between a-Stieltjes and canonical Hankel parametrization
7. Connection between right a- and right ß-Stieltjes parametrizations
Appendix A. Moore-Penrose inverse
Appendix B. Some considerations on non-negative Hermitian measures
References
On Maximal Weight Solutions of a Moment Problem for Rational Matrix-valued Functions
0. Introduction
1. Preliminaries
2. Some basics on canonical solutions of Problem (R)
3. A special family of solutions of Problem (R)
4. Characterizations of F(a)n,u in the set of canonical solutions
5. An extremal property of F(a)n,u in the solution set of Problem (R)
6. Some conclusions from Theorem 5.5
References

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