Umfang:
Online-Ressource (V, 300 p, digital)
ISBN:
9783034804288
,
1283625032
,
9781283625036
Serie:
Operator Theory: Advances and Applications 226
Inhalt:
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Anmerkung:
Description based upon print version of record
,
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,κ and reciprocal sequences; 6. Further observations on invertible sequences; 7. Some considerations on EP sequences
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8. Moore-Penrose pseudoinverses of holomorphic matrix-malued functionsAppendix 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
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4. Reciprocal sequences5. 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,κ; 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
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Appendix B. On two particular multiplicative groups of triangular block matricesReferences; 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 α-Stieltjes One-sided Non-negative Definite Sequences
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7. Moore-Penrose Inverses of Matricial Carathéodory Functions8. 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
Weitere Ausg.:
ISBN 9783034804271
Weitere Ausg.:
Buchausg.: Alpay, Daniel, 1956 - Interpolation, Schur functions and moment problems II Basel : Birkhäuser, 2012 ISBN 9783034804271
Sprache:
Englisch
DOI:
10.1007/978-3-0348-0428-8
URL:
Volltext
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URL:
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Mehr zum Autor:
Alpay, Daniel 1956-
