Skip to main content
SpringerLink
Log in

On Carleman formulas for the Dolbeault Cohomology

  • Published:
Annali dell’Università di Ferrara Aims and scope Submit manuscript

Abstract

We discuss the Cauchy problem for the Dolbeault cohomology in a domain of Cn with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.

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

  • [AD75]L. A. Aizenberg—Sh. A. Dautov,Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties, Amer. Math. Soc., Providence, R.I., 1983.

    MATH  Google Scholar 

  • [AG62]A. Andreotti—H. Grauert,Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France,90 (1962), 193–259.

    MATH  MathSciNet  Google Scholar 

  • [AH72a]A. Andreotti—C. D. Hill,E. E. Levi convexity and the Hans Lewy problem. Part 1: Reduction to vanishing theorems, Ann. Scuola Norm. Super. Pisa,26, no. 3 (1972), 325–363.

    MATH  MathSciNet  Google Scholar 

  • [AH72b]A. Andreotti—C. D. Hill,E. E. Levi convexity and the Hans Lewy problem. Part 2: Vanishing theorems, Ann. Scuola Norm. Super. Pisa,26, no. 4 (1972), pp. 747–806.

    MATH  MathSciNet  Google Scholar 

  • [Aiz93]L. A. Aizenberg,Carleman Formulas in Complex Analysis. First Applications, Kluwer Academic Publishers, Dordrecht NL, 1993, 358 pp.

    Google Scholar 

  • [AT90]L. A. Aizenberg—N. N. Tarkhanov,Conditionally stable problems and Carleman formulas, Sibirsk. Mat. Zh.,31, no. 6 (1990), pp. 9–15.

    MathSciNet  Google Scholar 

  • [Ker72]N. Kerzman,The Bergman kernel function. Differentiability at the boundary, Math. Ann.,195, no. 2 (1972), pp. 149–158.

    MathSciNet  Google Scholar 

  • [Kop67]W. Koppelman,The Cauchy integral for differential forms, Bull. Amer. Math. Soc.,73 no. 4 (1967), pp. 554–556.

    Article  MATH  MathSciNet  Google Scholar 

  • [Lau75]H. Laufer,On the infinite dimensionality of the Dolbeault cohomology groups, Proc. AMS,52 (1975), pp. 293–296.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ran86]R. M. Range,Holomorphic Functions and Integral Representations in Several Complex Variables, Graduate Texts in Mathematics (No 108), Springer-Verlag, Berlin et al., 1986.

    MATH  Google Scholar 

  • [Tar95]N. N. Tarkhanov,Complexes of Differential Operators, Kluwer Academic Publishers, Dordrecht, NL, 1995.

    MATH  Google Scholar 

Download references

Author information

Author notes

  1. Mauro Nacinovich

    Present address: Dipartimento di Matematica, Via F. Buonarroti 2, 56127, Pisa, Italy

  2. Bert-Wolfgang Schulze

    Present address: Institut für Mathematik, Universität Potsdam, Postfach 60 15 53, 14415, Potsdam, Germany

  3. Nikolai Tarkhanov

    Present address: Institute of Physics, Russian Academy of Sciences, Akademgorodok, 660036, Krasnovarsk, Russia

Authors and Affiliations

    Authors
    1. Mauro Nacinovich
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. Bert-Wolfgang Schulze
      View author publications

      You can also search for this author in PubMed Google Scholar

    3. Nikolai Tarkhanov
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    To the memory of Lamberto Cattabriga

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Nacinovich, M., Schulze, BW. & Tarkhanov, N. On Carleman formulas for the Dolbeault Cohomology. Ann. Univ. Ferrara 45, 253–262 (1999). https://doi.org/10.1007/BF02826098

    Download citation

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF02826098

    AMS subject classification

    Search

    Navigation