Gleason’s problem associated to the fractional Cauchy-Riemann operator, Fueter series, Drury-Arveson space and related topics

Alpay, D.; Cerejeiras, P.; Kähler, U.

doi:10.1090/proc/13613

Gleason’s problem associated to the fractional Cauchy-Riemann operator, Fueter series, Drury-Arveson space and related topics
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by D. Alpay, P. Cerejeiras and U. Kähler PDF

Proc. Amer. Math. Soc. 145 (2017), 4821-4835 Request permission

Abstract:

In this paper we present the building blocks for a function theory based on fractional Cauchy-Riemann operators. We are going to construct basic monogenic powers and Fueter series. With these tools we are going to study Gleason’s problem and reproducing kernel spaces, like the Drury-Arveson space and de Branges-Rovnyak spaces. We end with a statement on Schur multipliers in this setting.

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