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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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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


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
  • MR Author ID: 223612
  • Email:
  • 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
  • MR Author ID: 635235
  • Email:
  • 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:
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4821-4835
  • MSC (2010): Primary 30G35; Secondary 26A33, 30A05, 31B05
  • DOI:
  • MathSciNet review: 3691998