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
Partially supported by the G.N.S.A.G.A. of the Italian C.N.R.
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© 1987 Springer-Verlag
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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. https://doi.org/10.1007/BFb0078962
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DOI: https://doi.org/10.1007/BFb0078962
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Print ISBN: 978-3-540-18357-0
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