A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions.

Damir Z. Arov is Professor of Mathematical Analysis at South-Ukraine Pedagogical University in Odessa. He is the author of more than 100 research and survey papers and has been an invited speaker at numerous international conferences.

Preface; 1. Introduction; 2. Algebraic preliminaries; 3. The Nevanlinna class of meromorphic mvf's; 4. J-contractive and J-inner matrix valued functions; 5. Reproducing kernel Hilbert spaces; 6. Generalized interpolation problems; 7. Generalized Krein extension problems; 8. Darlington representations and related inverse problems; 9. More criteria for strong regularity; 10. Formulas for entropy functionals; Bibliography.