Contents

1. Introduction 1

2. Preliminaries 7

3. Fundamental matrix inequalities 12

4. On H{Q) spaces 18

5. Parametrizations of all solutions 23

6. The equality case 29

7. Nontangential limits 32

8. The Nevanlinna-Pick boundary problem 41

9. A multiple analogue of the Caratheodory-Julia theorem 48

10. On the solvability of a Stein equation 65

11. Positive definite solutions of the Stein equation 76

12. A Caratheodory-Fejer boundary problem 80

13. The full matrix Caratheodory-Fejer boundary problem 87

14. The lossless inverse scattering problem 94

Bibliography 105