2015
DOI: 10.1080/17476933.2015.1113270
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Slice regular composition operators

Abstract: In the article the class of slice regular functions is shown to be closed under a new regular composition. The new regular composition turns out to be globally defined in contrast to the locally defined version by Vlacci. Its advantage over Vlacci's is demonstrated by its associated theory of composition operators and dynamical systems for slice regular functions. Especially, the corresponding Littlewood subordination principle and the Denjoy-Wolff type theorem can be established.2010 Mathematics Subject Class… Show more

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Cited by 15 publications
(6 citation statements)
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“…Recalling equality in (2.8), an orthogonality consideration gives We begin with a notion of regular diameter, which is intimately related to a new regular composition (cf. [35]). w n a n .…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
See 1 more Smart Citation
“…Recalling equality in (2.8), an orthogonality consideration gives We begin with a notion of regular diameter, which is intimately related to a new regular composition (cf. [35]). w n a n .…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
“…Now the desired equality (3.17 We begin with a notion of regular diameter, which is intimately related to a new regular composition (cf. [35]).…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
“…Indeed, one can define an exponential map exp : H → H \ {0} on the quaternions which turns out to be slice regular and slice preserving. Nonetheless, in general the composition of slice regular functions is not slice regular (for a more detailed treatment of the composition in the setting of slice regular functions see [9,18,19]). Thus, considering exp •f for any slice regular function f provides a never vanishing function which could be non-regular.…”
Section: Introductionmentioning
confidence: 99%
“…Given f ∈ SR(Ω) the composition exp •f is not always slice-regular. In [5], Colombo, Sabadini and Struppa gave the following definition which coincides with exp •f if f ∈ SR R (Ω) (see also [12] and [13], where several different regular compositions are introduced).…”
Section: Introductionmentioning
confidence: 99%