Skip to main content
SpringerLink
Log in

Cauchy problems with monogenic initial values

  • Conference paper
  • First Online:
Analytic Functions Błażejewko 1982

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1039))

  • 462 Accesses

Abstract

Using an abstract version of the Cauchy-Kovalevska theorem, the initial value problem (∂/∂t)w=Lw, w(x,o)=wo(x) is solved, where the initial function wo=wo(x) is monogenic in x and L transforms the set of all monogenic functions into itself; t being a real variable. The constructed solution is monogenic for every t.

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. BERS, L.: Theory of pseudo-analytic functions, New York University, 1953.

    Google Scholar 

  2. DELANGHE, R. and F. BRACKX: Hypercomplex function theory and Hilbert modules with reproducing kernel, Proc. London Math. Soc. 37 (1978), 545–576.

    Article  MathSciNet  MATH  Google Scholar 

  3. GOLDSCHMIDT, B.: Verallgemeinerte analytische Vektoren im Rn, Universität Halle, B-Dissertationsschrift, Halle (Saale) 1980.

    Google Scholar 

  4. —: Properties of generalized analytic vectors in Rn, Math. Nachr. 103 (1981), 245–254.

    Article  MathSciNet  MATH  Google Scholar 

  5. МАНДЖАВИДЖЕ, Т.Ф. и В. ТУЧКЕ: Некоторые оценки норм проиэводных голоморфных функций в подобластях и одно применение к эадачам с начальными эначениями, ZAA, in print.

    Google Scholar 

  6. ОВСЯннИКОВ, Л.В.: Жадача Кощи в щколе банаховых пространств аналитических функций. Труды симпоэиума по механике сплощной среды и родственным проблемам аналиэа II, Тбилиси 1971, pp. 219–229.

    Google Scholar 

  7. SOMMEN, F.: Some connections between Clifford analysis and complex analysis. Complex variables: Theory and application, to appear.

    Google Scholar 

  8. TRÈVES, F.: Basic linear partial differential equations, New York — San Francisco — London 1975.

    Google Scholar 

  9. TUTSCHKE, W.: Partielle komplexe Differentialgleichungen in einer und in mehreren komplexen Variablen, Berlin 1977.

    Google Scholar 

  10. [10] —: Vorlesungen über partielle Differentialgleichungen, Leipzig 1978.

    Google Scholar 

  11. —: Жадача с начальными эначениями для обобшенных аналитических функций, эависяших от времени, ДАН ССР 262, No.5(1982), 1081–1085.

    Google Scholar 

  12. —: Потенциальные векторы, эависяшие от времени. Труды симпоэиума по случаю 75-летия со дня рождения академика И.Н. Векуа, Тбилиси 1982, in print.

    Google Scholar 

  13. —: Ассоциированные операторы комплексного аналиэа, Сообш. АН Груэ. ССР, 107 (1982), 481–484.

    MATH  Google Scholar 

  14. —: Рещение эадачи Кощи в классах функций, являюшихся пространственными обобшениями обобшенных аналитических функций, in preparation.

    Google Scholar 

  15. — and C. WITHALM: The Cauchy-Kovalevska theorem for pseudoholomorphic functions in the sense of L. Bers. Complex variables: Theory and applications, in print.

    Google Scholar 

  16. VEKUA, I. N.: Verallgemeinerte analytische Funktionen [trans. from Russian], Berlin 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion-Mathematik der Martin-Luther-Universität Halle-Wittenberg, Universitätsplatz 8/9, DDR-4020, Halle an der Saale, DDR

    Wolfgang Tutschke

Authors
  1. Wolfgang Tutschke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Łódź Branch, Narutowicza 56, 90-136, Łódź, Poland

    Julian Ławrynowicz

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tutschke, W. (1983). Cauchy problems with monogenic initial values. In: Ławrynowicz, J. (eds) Analytic Functions Błażejewko 1982. Lecture Notes in Mathematics, vol 1039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073386

Download citation

  • DOI: https://doi.org/10.1007/BFb0073386

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12712-3

  • Online ISBN: 978-3-540-38697-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation