Skip to main content
SpringerLink
Log in

Function Theory Over Non-symmetric Slice Domains

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

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

  • 470 Accesses

Abstract

This chapter turns back to the study of regular functions \(f : \Omega \to {\mathbb {H}}\) initiated in Sect. 1.1. While Chaps. 3–9 focused on the case when Ω is a symmetric slice domain, we now consider slice domains in general (dropping the symmetry hypothesis).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. X. Dou, G. Ren, Riemann slice-domains over quaternions I (2018). Preprint arXiv:1808.06994 [math.CV]

    Google Scholar 

  2. X. Dou, G. Ren, Riemann slice-domains over quaternions II (2018). Preprint arXiv:1809.07979 [math.CV]

    Google Scholar 

  3. X. Dou, G. Ren, I. Sabadini, Extension theorem and representation formula in non-axially symmetric domains for slice regular functions (2020). arXiv:2003.10487 [math.CV]

    Google Scholar 

  4. G. Gentili, C. Stoppato, Geometric function theory over quaternionic slice domains. J. Math. Anal. Appl. 495(2), 124780 (2021)

    Google Scholar 

  5. R. Ghiloni, A. Perotti, Slice regular functions on real alternative algebras. Adv. Math. 226(2), 1662–1691 (2011)

    Article  MathSciNet  Google Scholar 

  6. R. Ghiloni, A. Perotti, Volume Cauchy formulas for slice functions on real associative *-algebras. Complex Var. Elliptic Equat. 58(12), 1701–1714 (2013)

    Article  MathSciNet  Google Scholar 

  7. R. Ghiloni, C. Stoppato, Quaternionic slice regularity beyond slice domains. Preprint http://hdl.handle.net/2158/1274664

  8. R. Ghiloni, A. Perotti, C. Stoppato, Singularities of slice regular functions over real alternative ∗-algebras. Adv. Math. 305, 1085–1130 (2017)

    Article  MathSciNet  Google Scholar 

  9. R. Ghiloni, A. Perotti, C. Stoppato, Division algebras of slice functions. Proc. Roy. Soc. Edinburgh Sect. A 150(4), 2055–2082 (2020)

    Article  MathSciNet  Google Scholar 

  10. R. Ghiloni, A. Perotti, C. Stoppato, Slice regular functions and orthogonal complex structures over \({\mathbb {R}} ^8\). J. Noncommut. Geom. 16(2), 637–676 (2022)

    Google Scholar 

  11. A. Perotti, A local Cauchy integral formula for slice-regular functions (2021). Preprint arXiv:2105.07041 [math.CV]

    Google Scholar 

  12. A. Perotti, Cauchy-Riemann operators and local slice analysis over real alternative algebras. J. Math. Anal. Appl. 516(1), 126480 (2022)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept of Math and Computer Science, University of Florence, Florence, Italy

    Graziano Gentili & Caterina Stoppato

  2. Donald Bren Presidential Chair in Math, Chapman University, Orange, CA, USA

    Daniele C. Struppa

Authors
  1. Graziano Gentili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Caterina Stoppato
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniele C. Struppa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Gentili, G., Stoppato, C., Struppa, D.C. (2022). Function Theory Over Non-symmetric Slice Domains. In: Regular Functions of a Quaternionic Variable. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-07531-5_11

Download citation

Publish with us

Policies and ethics

Search

Navigation