Orthogonal Matrix-valued Polynomials and Applications

I. Gohberg

ISBN 10: 3034854749 / ISBN 13: 9783034854740

Editore: Birkhäuser Basel, Springer Basel Aug 2014, 2014

Riguardo questo articolo

Neuware -This paper is a largely expository account of the theory of p x p matrix polyno mials associated with Hermitian block Toeplitz matrices and some related problems of interpolation and extension. Perhaps the main novelty is the use of reproducing kernel Pontryagin spaces to develop parts of the theory in what hopefully the reader will regard as a reasonably lucid way. The topics under discussion are presented in a series of short sections, the headings of which give a pretty good idea of the overall contents of the paper. The theory is a rich one and the present paper in spite of its length is far from complete. The author hopes to fill in some of the gaps in future publications. The story begins with a given sequence h_n' . , hn of p x p matrices with h-i = hj for j = 0, . , n. We let k = O, . ,n, (1.1) denote the Hermitian block Toeplitz matrix based on ho, . , hk and shall denote its 1 inverse H k by (k)] k [ r = . k = O, . ,n, (1.2) k II} . '-0 ' I- whenever Hk is invertible.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 228 pp. Englisch.

Codice articolo 9783034854740

Dati bibliografici

• Titolo: Orthogonal Matrix-valued Polynomials and Applications
• Editore: Birkhäuser Basel, Springer Basel Aug 2014
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 3034854749
• ISBN 13: 9783034854740
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 244 L x 170 A x 13 P (millimetri) 244 millimetri di larghezza per 170 millimetri di altezza per 13 millimetri di profondità
• Peso: 402 grammi

Descrizione articolo

Riassunto

This paper is a largely expository account of the theory of p x p matrix polyno­ mials associated with Hermitian block Toeplitz matrices and some related problems of interpolation and extension. Perhaps the main novelty is the use of reproducing kernel Pontryagin spaces to develop parts of the theory in what hopefully the reader will regard as a reasonably lucid way. The topics under discussion are presented in a series of short sections, the headings of which give a pretty good idea of the overall contents of the paper. The theory is a rich one and the present paper in spite of its length is far from complete. The author hopes to fill in some of the gaps in future publications. The story begins with a given sequence h_n" ... , hn of p x p matrices with h-i = hj for j = 0, ... , n. We let k = O, ... ,n, (1.1) denote the Hermitian block Toeplitz matrix based on ho, ... , hk and shall denote its 1 inverse H k by (k)] k [ r = .. k = O, ... ,n, (1.2) k II} . '-0 ' I- whenever Hk is invertible.

Contenuti

Bibliography of Mark Grigor’Evich Krein.- On Orthogonal Matrix Polynomials.- n-Orthonormal Operator Polynomials.- Extension of a Theorem of M. G. Krein on Orthogonal Polynomials for the Nonstationary Case.- Hermitian Block Toeplitz Matrices, Orthogonal Polynomials, Reproducing Kernel Pontryagin Spaces, Interpolation and Extension.- Matrix Generalizations of M. G. Krein Theorems on Orthogonal Polynomials.- Polynomials Orthogonal in an Indefinite Metric.