Holomorphic Operator Functions of One Variable and Applications

1. Elementary properties of holomorphic functions

2. Solution of
bar partial u = f
and applications

3. Splitting and factorization with respect to a contour

4. The Rouché theorem for operator functions

5. Multiplicative cocycles (
mathcal{O}^G
-cocycles)

6. Families of subspaces

7. Plemelj-Muschelishvili factorization

8. Wiener-Hopf operators, Toeplitz operators and factorization

9. Multiplicative cocycles with restrictions (
mathcal{F}
-cocycles)

10. Generalized interpolation problems

11. Holomorphic equivalence, linearization and diagonalization

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