Skip to main content
SpringerLink
Log in

An extremum problem related to Morera's theorem

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The property of being holomorphic is studied for a continuous function whose integrals over the boundaries of the triangles from a specified set are zero. The results substantially strengthen Morera's and Dzyadyk's well-known theorems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. A. Berenstein and R. Gay, “Le problème de Pompeiu local,”J. Anal. Math.,52, 133–166 (1989).

    MathSciNet  Google Scholar 

  2. C. A. Berenstein and D. Struppa, “Complex analysis and convolution equations,” in:Itogi Nauki i Tekniki. Sovrem. Problemy Matem. Fundament. Napravleniya [in Russian] Vol. 54, VINITI, Moscow (1989), pp. 5–111.

    Google Scholar 

  3. V. V. Volchkov, “Functions with zero integrals over some sets,”Dokl. Akad. Nauk Ukr. SSR. Ser. A., No. 8, 9–11 (1990).

    MATH  MathSciNet  Google Scholar 

  4. V. V. Volchkov,Functions with Zero Integrals over Some Sets, deposited in UkrNIINTI, No. 1748-Uk90, Donetsk State University, Donetsk (1990).

    Google Scholar 

  5. V. V. Volchkov,Some Questions Related to the Pompeiu Problem, deposited in GNTB of Ukraine, Donetsk State University, Donetsk (1993).

    Google Scholar 

  6. V. V. Volchkov, “Morera type theorems in domains with weak cone condition,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. J. (Iz. VUZ)], No. 10, 15–20 (1993).

    MATH  MathSciNet  Google Scholar 

  7. V. K. Dzyadyk, “A geometric definition of analytic functions,”Uspekhi Mat. Nauk [Russian Math. Surveys],15, No. 1, 191–194 (1960).

    MATH  Google Scholar 

  8. V. V. Volchkov, “Pompeiu type problems on manifolds,”Dokl. Akad. Nauk Ukraine, No. 11, 9–12 (1993).

    MATH  MathSciNet  Google Scholar 

  9. V. V. Volchkov, “A Zalcman problem and generalizations,”Mat. Zametki [Math. Notes],53, No. 2, 30–36 (1993).

    MATH  MathSciNet  Google Scholar 

  10. V. V. Volchkov, “Morera type theorems on the unit disk,”Anal. Math.,20, 49–63 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  11. C. A. Berenstein, D. C. Chang, D. Pascuas, and L. Zalcman, “Variations on the theorem of Morera,”Contemp. Math.,137, 63–78 (1992).

    MathSciNet  Google Scholar 

  12. A. A. Kirillov and A. D. Gvishiani,Theorems and Problems of Functional Analysis [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  13. S. Helgason,Groups and Geometric Analysis, Academic Press, Orlando-San Diego-San Francisko-New York-London (1984).

    Google Scholar 

  14. A. F. Timan and V. N. Trofimov,Introduction to the Theory of Harmonic Functions [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  15. L. Hörmander,Linear Partial Differential Operators, New York (1963).

Download references

Author information

Authors and Affiliations

  1. Donetsk State University, USSR

    V. V. Volchkov

Authors
  1. V. V. Volchkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 804–809, December, 1996.

This research was supported by the International Science Foundation under grants No. U9D000 and No. U9D200.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volchkov, V.V. An extremum problem related to Morera's theorem. Math Notes 60, 606–610 (1996). https://doi.org/10.1007/BF02305151

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02305151

Key words

Search

Navigation