Elementary properties of holomorphic functions.- Solution of and applications.- Splitting and factorization with respect to a contour.- The Rouché theorem for operator functions.- Multiplicative cocycles ( -cocycles).- Families of subspaces.- Plemelj-Muschelishvili factorization.- Wiener-Hopf operators, Toeplitz operators and factorization.- Multiplicative cocycles with restrictions ( -cocycles).- Generalized interpolation problems.- Holomorphic equivalence, linearization and diagonalization.

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