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Silva-holomorphy types, borel transforms and partial differential operators

Part of the Lecture Notes in Mathematics book series (LNM,volume 843)

Abstract

Dineen in [2] described and studied various topological vector spaces of holomorphic functions and introduced the α-holomorphy, α-β-holomorphy and α-β-γ-holomorphy types solving questions about Borel transforms, convolution and partial differential operators. Matos & Nachbin in working with Silva-holomorphic functions between two complex locally spaces defined Silva-holomorphy types ϑ and obtained results about Borel transforms and Malgrange's theorem for convolution operators. In this work, using the techniques developed in [2] and using the study of the Silva-holomorphic functions in complex locally convex spaces, we generalize the results presented by Dineen in [2].

Keywords

  • Compact Subset
  • Taylor Series Expansion
  • Topological Vector Space
  • Formal Power Series
  • Partial Differential Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Barroso, J.A., Topologia nos espaços de aplicações holomorfas entre espaços localmente convexos, Anais da Academia Brasileira de Ciências, Vol. 43 (1971).

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  2. Dineen, S., Holomorphy types on Banach space, Studia Mathematica, T. XXXIX. (1971).

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  3. Kothe, G., Topological Vector Spaces I, Springer-Verlag, Berlin, Heidelberg, New York, 1969.

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  4. Matos, M.C. & Nachbin, L., Silva-holomorphy types (to appear in these Proceedings).

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  5. Nachbin, L., Holomorfia em dimensão infinita, Lectures Notes, Universidade Estadual de Campinas, 1976.

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  6. Paques, O.T.W., Tensor Products of Silva-holomorphic Functions, Advances in Holomorphy, North-Holland, 1977.

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© 1981 Springer-Verlag

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Bianchini, M. (1981). Silva-holomorphy types, borel transforms and partial differential operators. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089270

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  • DOI: https://doi.org/10.1007/BFb0089270

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10560-2

  • Online ISBN: 978-3-540-38529-5

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