
Orthogonal Matrix-valued Polynomials and Applications
Seminar on Operator Theory at the School of Mathematical Sciences, Tel Aviv University
I. Gohberg(Author)
Birkhäuser (Publisher)
Published on 23. August 2014
Book
Paperback/Softback
IX, 214 pages
978-3-0348-5474-0 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1988
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
IX, 214 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 13 mm
Weight
402 gr
ISBN-13
978-3-0348-5474-0 (9783034854740)
DOI
10.1007/978-3-0348-5472-6
Schweitzer Classification
Other editions
Additional editions
Izrael Gohberg
Orthogonal Matrix-valued Polynomials and Applications
Seminar on Operator Theory at the School of Mathematical Sciences, Tel Aviv University
Book
09/1988
Birkhäuser Verlag GmbH
€75.67
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Content
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.