Slice Hyperholomorphic Schur Analysis

Part I. Classical Schur Analysis

1. Preliminaries
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

2. Rational Functions
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

3. Schur Analysis
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Part II. Quaternionic Analysis

4. Finite-dimensional Preliminaries
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

5. Quaternionic Functional Analysis
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

6. Slice Hyperholomorphic Functions
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

7. Operator-valued Slice Hyperholomorphic Functions
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Part III. Quaternionic Schur Analysis

8. Reproducing Kernel Spaces and Realizations
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

9. Rational Slice Hyperholomorphic Functions
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

10. First Applications: Scalar Interpolation and First-order Discrete Systems
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

11. Interpolation: Operator-valued Case
Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Keywords: Mathematics, Functions of a Complex Variable, Functional Analysis, Operator Theory