Advertisement

Sections of coherent analytic sheaves with growth on complex spaces

  • 24 Accesses

Summary

In this paper we will be concerned with a type of growth of sections of cohernet analytic sheaves which is an extension of polynomial growth. On bounded domains this type of growth almost coincides with that given in Hörmander [5] and it enables us to extend a result of R. Narasimhan [7] and Y. T. Siu [8]. The result (Theorem2.1 below) looks like Theorem1 in [7] but it is the method in [8] that is amenable to extension. As in [7], [8], for domains of holomorphy in Cn, the result is derived from L2-estimates of the\(\bar \partial \)-operator after establishing an infinitely differentiable version.

References

  1. [1]

    P. W. Darko, Lp-estimates of the\(\bar \partial \)-operator and sections with growth, Thesis, Cornell University, 1971.

  2. [2]

    R. C. Gunning -H. Rossi,Analytic functions of several complex variables, Englewood Cliffs, Prentice Hall, New Jersey, 1965.

  3. [3]

    L. Hörmander, L2-estimates and existence theorems for the\(\bar \partial \)-operator, Acta Math.,113 (1965), pp. 89–152.

  4. [4]

    L. Hörmander,An introduction to complex analysis in several variables, D. Van Nostrand, Princeton, New Jersey, 1966.

  5. [5]

    L. Hörmander,Generators for some rings of analytic functions, Bull. Amer. Math. Soc.,73 (1967), pp. 943–949.

  6. [6]

    R. Narasimhan,On holomorphic functions of polynomial growth in a bounded domain, Scuola Normale Superiore, Pisa, Serie III, no. 21, 1967.

  7. [7]

    R. Narasimhan,Cohomology with bounds on complex spaces, Lecture Notes in Mathematics, no. 155, Springer-Verlag, pp. 141–150, 1970.

  8. [8]

    Y. T. Siu,On holomorphic functions of polynomial growth in a bounded domain, Duke Math. Journal (1970).

Download references

Author information

Additional information

Entrata in Redazione il 12 luglio 1973.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Darko, P.W. Sections of coherent analytic sheaves with growth on complex spaces. Annali di Matematica 104, 283–295 (1975) doi:10.1007/BF02417020

Download citation

Keywords

  • Complex Space
  • Polynomial Growth
  • Analytic Sheave
  • Coherent Analytic Sheave
  • Differentiable Version