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Slice monogenic functions

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Abstract

In this paper we offer a new definition of monogenicity for functions defined on ℝn+1 with values in the Clifford algebra ℝ n following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra ℝ n . We will prove a Cauchy integral formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials and power series.

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References

  1. F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Resarch Notes in Math., 76, Pitman (Advanced Publishing Program), Boston, MA, 1982.

    MATH  Google Scholar 

  2. F. Colombo, I. Sabadini, F. Sommen and D. C. Struppa, Analysis of Dirac Systems and Computational Algebra, Progress in Mathematical Physics, Vol. 39, Birkhäuser, Boston, 2004.

    Google Scholar 

  3. F. Colombo, I. Sabadini and D. C. Struppa, A new functional calculus for noncommuting operators, Journal of Functional Analysis 254 (2008), 2255–2274.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. G. Cullen, An integral theorem for analytic intrinsic functions on quaternions, Duke Mathematical Journal 32 (1965), 139–148.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Delanghe, F. Sommen and V. Soucek, Clifford Algebra and Spinor-valued Functions, Mathematics and Its Applications 53, Kluwer Academic Publishers Group, Dordrecht 1992.

    MATH  Google Scholar 

  6. G. Gentili and D. C. Struppa, A new approach to Cullen-regular functions of a quaternionic variable, Comptes Rendus Mathématique Académie des Sciences. Paris, 342 (2006), 741–744.

    MATH  MathSciNet  Google Scholar 

  7. G. Gentili and D. C. Struppa, A new theory of regular functions of a quaternionic variable, Advances in Mathematics 216 (2007), 279–301.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Gentili and D. C. Struppa, Regular functions on a Clifford Algebra, Complex Variables and Elliptic Equations 53 (2008), 475–483.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Y. Lam, A First Course in Noncommutative Rings, 2nd edition, Graduate Texts in Mathematics, Vol. 131 Springer-Verlag, New York, 2001.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133, Milano, Italy

    Fabrizio Colombo & Irene Sabadini

  2. Department of Mathematics and Computer Sciences, Chapman University, Orange, CA, 92866, USA

    Daniele C. Struppa

Authors
  1. Fabrizio Colombo
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  2. Irene Sabadini
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  3. Daniele C. Struppa
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Correspondence to Fabrizio Colombo.

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Colombo, F., Sabadini, I. & Struppa, D.C. Slice monogenic functions. Isr. J. Math. 171, 385–403 (2009). https://doi.org/10.1007/s11856-009-0055-4

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  • DOI: https://doi.org/10.1007/s11856-009-0055-4

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