Skip to main content

Integral Representations

  • Chapter
  • First Online:
Regular Functions of a Quaternionic Variable

Part of the book series: Springer Monographs in Mathematics ((SMM))

  • 1306 Accesses

Abstract

Regular quaternionic functions inherit a version of the Cauchy Theorem from the holomorphic complex functions. Let us begin with some notations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. F. Colombo, G. Gentili, I. Sabadini, A Cauchy kernel for slice regular functions. Ann. Global Anal. Geom. 37(4), 361–378 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Colombo, I. Sabadini, A structure formula for slice monogenic functions and some of its consequences, in Hypercomplex Analysis, ed. by I. Sabadini, M. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 101–114

    Google Scholar 

  3. F. Colombo, I. Sabadini, D.C. Struppa, The Pompeiu formula for slice hyperholomorphic functions. Mich. Math. J. 60(1), 163–170 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. J.B. Conway, Functions of one complex variable. Graduate Texts in Mathematics, vol. 11, 2nd edn. (Springer, New York, 1978)

    Google Scholar 

  5. G. Gentili, D.C. Struppa, A new theory of regular functions of a quaternionic variable. Adv. Math. 216(1), 279–301 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Stoppato, Regular functions of one quaternionic variable. Ph.D. thesis, advisor G. Gentili, Università degli Studi di Firenze, 2010

    Google Scholar 

  7. C. Stoppato, Singularities of slice regular functions. Math. Nachr. 285(10), 1274–1293 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Vlacci, The argument principle for quaternionic slice regular functions. Mich. Math. J. 60(1), 67–77 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gentili, G., Stoppato, C., Struppa, D.C. (2013). Integral Representations. In: Regular Functions of a Quaternionic Variable. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33871-7_6

Download citation

Publish with us

Policies and ethics