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  and it enables us to extend a result of R. Narasimhan  and Y. T. Siu . The result (Theorem2.1 below) looks like Theorem1 in  but it is the method in  that is amenable to extension. As in , , for domains of holomorphy in Cn, the result is derived from L2-estimates of the\(\bar \partial \)-operator after establishing an infinitely differentiable version.
P. W. Darko, Lp-estimates of the\(\bar \partial \)-operator and sections with growth, Thesis, Cornell University, 1971.
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Y. T. Siu,On holomorphic functions of polynomial growth in a bounded domain, Duke Math. Journal (1970).
Entrata in Redazione il 12 luglio 1973.
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Darko, P.W. Sections of coherent analytic sheaves with growth on complex spaces. Annali di Matematica 104, 283–295 (1975) doi:10.1007/BF02417020
- Complex Space
- Polynomial Growth
- Analytic Sheave
- Coherent Analytic Sheave
- Differentiable Version