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Reproducing kernel spaces of series of Fueter polynomials. (English) Zbl 1107.46023
Förster, Karl-Heinz (ed.) et al., Operator theory in Krein spaces and nonlinear eigenvalue problems. Selected papers of the 3rd workshop, TU Berlin, Germany, December 12–14, 2003. Basel: Birkhäuser (ISBN 3-7643-7452-7/hbk). Operator Theory: Advances and Applications 162, 19-45 (2006).
Summary: We study reproducing kernel spaces of power series of Fueter polynomials and their multipliers. In particular, we prove a counterpart of the Beurling–Lax theorem in the quaternionic Arveson space and we define and characterize counterparts of the Schur–Agler classes. We also address the notion of rationality in the hyperholomorphic setting.
For the entire collection see [Zbl 1086.47006].

46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
30G99 Generalized function theory