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Quantization and Infinite-Dimensional Systems pp 109–112Cite as

On Reproducing Kernels for Holomorphic Vector Bundles

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Abstract

We introduce (1) the reproducing kernels of Bergman type for holomorphic sections of complex hermitian vector bundles, and (2) the maps defined by these kernels on total and base spaces of considered bundles into some Hilbert and Grassmann spaces. We present (without proofs) the main results concerning basic properties of the introduced objects.

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References

  1. Z. Pasternak-Winiarski, Bergman spaces and kernels for holomorphic vector bundles, Preprint.

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  2. Z. Pasternak-Winiarski, Maps on complex manifolds into Grassmann spaces defined by reproducing kernels of Bergman type, in preparation.

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  3. Z. Pasternak-Winiarski, Reproducing kernels and embedding theorems for complex manifolds, in preparation.

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  4. S.G. Krantz, “Function theory of several complex variables”, Interscience-Wiley, New York (1982).

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  5. Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Inter nal J. Math. &Math. Sci. ,15:1 (1992).

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  6. Z. Pasternak-Winiarski, Admissible weights and weighted Bergman functions, in: “Function Spaces, Proceedings on the Second International Conference, Poznań 1989”, Teubner-Texte zur Mathematik, Bc. 120, Teubner, Stuttgart-Leipzig (1991).

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661, Warsaw, Poland

    Zbigniew Pasternak-Winiarski

Authors
  1. Zbigniew Pasternak-Winiarski
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Editor information

Editors and Affiliations

  1. Catholic University of Louvain, Louvain-la-Neuve, Belgium

    J-P. Antoine

  2. Concordia University, Montréal, Québec, Canada

    S. Twareque Ali

  3. Warsaw University, Białystok, Poland

    W. Lisiecki  & A. Odzijewicz  & 

  4. Bulgarian Academy of Sciences, Sofia, Bulgaria

    I. M. Mladenov

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© 1994 Springer Science+Business Media New York

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Pasternak-Winiarski, Z. (1994). On Reproducing Kernels for Holomorphic Vector Bundles. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization and Infinite-Dimensional Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2564-6_13

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  • DOI: https://doi.org/10.1007/978-1-4615-2564-6_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6095-7

  • Online ISBN: 978-1-4615-2564-6

  • eBook Packages: Springer Book Archive

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