This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Author(s): Daniel Alpay (Editor), Victor Vinnikov (Editor)
Edition: 1
Year: 2007
Language: English
Pages: 322
Contents......Page 6
Editorial Introduction......Page 7
The Transformation of Issai Schur and Related Topics in an Indefinite Setting......Page 10
1.1 Classical Schur analysis......Page 12
1.2 Generalized Schur and Nevanlinna functions......Page 16
1.3 Reproducing kernel Pontryagin spaces......Page 17
1.4 The general scheme......Page 19
1.5 Outline of the paper......Page 22
2.1 Reproducing kernel Pontryagin spaces......Page 24
2.2 Analytic kernels and Pick matrices......Page 25
2.3 Generalized Schur functions and the spaces P(s)......Page 28
2.4 Generalized Nevanlinna functions and the spaces L(n)......Page 32
3. Some classes of rational matrix functions......Page 34
3.1 Realizations and McMillan degree of rational matrix functions......Page 35
3.2 J-unitary matrix functions and the spaces P(Θ): the line case......Page 36
3.3 J-unitary matrix functions and the spaces P(Θ): the circle case......Page 41
3.4 Factorizations of J-unitary matrix functions......Page 44
3.5 Additional remarks and references......Page 49
4.1 Generalized Schur functions: z[sub(1)] ∈ D......Page 50
4.2 Generalized Schur functions: z[sub(1) ∈ T......Page 54
4.3 Generalized Nevanlinna functions: z[sub(1)] ∈ C[sup(+)]......Page 56
4.4 Generalized Nevanlinna functions: z[sub(1)] = ∞......Page 58
4.5 Additional remarks and references......Page 59
5.1 The Schur transformation......Page 60
5.2 The basic interpolation problem......Page 65
5.3 Factorization in the class U[sup(z1)][sub(c)]......Page 68
5.4 Realization......Page 71
5.5 Additional remarks and references......Page 73
6.1 The Schur transformation......Page 74
6.2 The basic boundary interpolation problem......Page 76
6.3 Factorization in the class U[sup(z1)][sub(c)]......Page 77
6.4 Additional remarks and references......Page 78
7.1 The Schur transformation......Page 79
7.2 The basic interpolation problem......Page 83
7.3 Factorization in the class U[sup(z1)][sub(l)]......Page 85
7.4 Realization......Page 87
7.5 Additional remarks and references......Page 90
8.1 The Schur transformation......Page 91
8.2 The basic boundary interpolation problem at ∞......Page 94
8.3 Factorization in the class U[sup(∞)][sub(l)]......Page 95
8.4 Realization......Page 97
8.5 Additional remarks and references......Page 99
References......Page 100
A Truncated Matricial Moment Problem on a Finite Interval. The Case of an Odd Number of Prescribed Moments......Page 108
On the Irreducibility of a Class of Homogeneous Operators......Page 174
Canonical Forms for Symmetric and Skewsymmetric Quaternionic Matrix Pencils......Page 208
Algorithms to Solve Hierarchically Semi-separable Systems......Page 264
Unbounded Normal Algebras and Spaces of Fractions......Page 304
