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


Authors: D. Alpay, P. Cerejeiras and U. Kähler
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 30G35; Secondary 26A33, 30A05, 31B05
DOI: https://doi.org/10.1090/proc/13613
Published electronically: May 30, 2017
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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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Additional Information

D. Alpay
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, POB653, Beer-Sheva 84105, Israel
Address at time of publication: Foster G. and Mary McGaw Professorship in Mathematical Sciences, Department of Mathematics, von Neumann Hall, Chapman University, Orange, California 92866
Email: alpay@chapman.edu

P. Cerejeiras
Affiliation: CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro Campus Universitário de Santiago 3810-193 Aveiro, Portugal
Email: pceres@ua.pt

U. Kähler
Affiliation: CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro Campus Universitário de Santiago 3810-193 Aveiro, Portugal
Email: ukaehler@ua.pt

DOI: https://doi.org/10.1090/proc/13613
Received by editor(s): July 27, 2016
Received by editor(s) in revised form: December 9, 2016
Published electronically: May 30, 2017
Additional Notes: The first author thanks the Earl Katz family for endowing the chair which supported his research. The work of the second and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/ 0416/2013.
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2017 American Mathematical Society