Herglotz functions: the Fueter variables case. (English) Zbl 07006570
Summary: In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz-Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.
MSC:
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
| 30G35 | Functions of hypercomplex variables and generalized variables |
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