Quaternionic de Branges Spaces and Characteristic Operator Function

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Focusing on quaternionic linear operators, this work explores their unique properties compared to complex operators, particularly in the noncommutative realm. It introduces concepts like the S-spectrum and S-resolvent operators while examining de Branges spaces, which serve as quaternionic analogs of analytic function spaces. The study emphasizes specific reproducing kernels in the unit ball or half-space of quaternions, delving into Hilbert, Pontryagin, and Krein spaces and their connections to operator models.