Convolutors in spaces of holomorphic functions

  • A. Meril
  • D. C. Struppa
Special Year Papers

DOI: 10.1007/BFb0078962

Part of the Lecture Notes in Mathematics book series (LNM, volume 1276)
Cite this paper as:
Meril A., Struppa D.C. (1987) Convolutors in spaces of holomorphic functions. In: Berenstein C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg

Abstract

Let Ω be an open convex set in ℂn and K a convex compact subset of Ωn: we provide sufficient, as well as necessary, conditions for the surjectivity of convolution operators between the spaces ℋ(Ω+K) and ℋ(Ω). Under natural hypotheses on the convolutors, we prove integral representation theorems for solutions f∈ℋ(Ω+K) of systems of homogeneous convolution equations. We apply this analysis to provide necessary and sufficient conditions for the hyperbolicity and the ellipticity of given systems of convolution equations; we also study the extension of solutions of homogeneous convolution equations to some sets which can be defined in terms of Ω, K and the convolutor.

Key words

Convolution equations holomorphic functions difference-differential equations AMS Subject Classification 32A15 42B99 43A45 

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. Meril
    • 1
  • D. C. Struppa
    • 2
  1. 1.Department de MathematiquesUniversitè de Bordeaux ITalenceFrance
  2. 2.Scuola Normale SuperiorePiazza dei Cavalieri, 7PisaItaly

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