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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2010, Issue 645

Issues

Duality theorems for slice hyperholomorphic functions

Fabrizio Colombo
  • Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133 Milano, Italy. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Irene Sabadini
  • Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133 Milano, Italy. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Daniele C. Struppa
  • Department of Mathematics and Computer Science, Schmid College of Science, Chapman University, Orange, CA 92866, USA. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-08-11 | DOI: https://doi.org/10.1515/crelle.2010.060

Abstract

The aim of this paper is to provide a characterization of the dual of the ℝn-module of slice monogenic functions on a class of compact sets in the Euclidean space . Despite the fact that the Cauchy formulas which are essential to such a characterization are based on different kernels, depending on whether one considers right or left slice monogenic functions, we are still able to establish a duality theorem which, since holomorphic functions are a very special case of slice monogenic functions, is the generalization of Köthe's theorem. The duality results are also obtained in the setting of quaternionic valued slice regular functions.

About the article

Received: 2008-10-20

Revised: 2009-03-31

Published Online: 2010-08-11

Published in Print: 2010-08-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2010, Issue 645, Pages 85–104, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2010.060.

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[1]
R. Ghiloni and A. Perotti
Advances in Mathematics, 2011, Volume 226, Number 2, Page 1662
[2]
Fabrizio Colombo, Irene Sabadini, and Daniele C. Struppa
Israel Journal of Mathematics, 2010, Volume 177, Number 1, Page 369
[3]
Fabrizio Colombo and Irene Sabadini
Journal of Geometry and Physics, 2010, Volume 60, Number 10, Page 1490
[4]
Daniel Alpay, Fabrizio Colombo, and Irene Sabadini
Integral Equations and Operator Theory, 2012, Volume 72, Number 2, Page 253
[5]
Fabrizio Colombo and Irene Sabadini
Complex Variables and Elliptic Equations, 2013, Volume 58, Number 1, Page 1
[6]
Fabrizio Colombo, Jose O. Gonzàles Cervantes, and Irene Sabadini
Mathematical Methods in the Applied Sciences, 2011, Volume 34, Number 15, Page 1896
[7]
Frank Sommen, Irene Sabadini, and Fabrizio Colombo
Communications on Pure and Applied Analysis, 2011, Volume 10, Number 4, Page 1165
[8]
Fabrizio Colombo, Irene Sabadini, and Frank Sommen
Mathematical Methods in the Applied Sciences, 2010, Volume 33, Number 17, Page 2050

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