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Cauchy Integral Formulas and Boundary Kernel Functions in Several Complex Variables

In: Proceedings of the Conference on Complex Analysis

Author

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  • L. Bungart

    (University of California, Department of Mathematics)

Abstract

In the present paper we attempt to coordinate some of the recent works concerned with the construction of domain-dependent Cauchy integral formulas in several complex variables, and then to point out an intimate relationship to boundary kernel functions. In particular, we are looking for formulas that are holomorphic in the parameters involved and not only real analytic as for instance the Bochner-Martinelli formula which has been established in [2] and [13]. The circle of ideas got probably started with the establishment of the so-called Cauchy-Weil formula in [15]. A somewhat related formula was later discussed by S. Bergman in [1] where also its relationship to boundary kernel functions is discussed. However, these formulas are valid only for domains with very special boundary properties. This prompted the search for a formula for any type of domain. The existence of such a formula has recently been established by A. Gleason [9] and the author [3], and to a certain extent also by O. Forster [8].

Suggested Citation

  • L. Bungart, 1965. "Cauchy Integral Formulas and Boundary Kernel Functions in Several Complex Variables," Springer Books, in: Alfred Aeppli & Eugenio Calabi & Helmut Röhrl (ed.), Proceedings of the Conference on Complex Analysis, pages 7-18, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-48016-4_2
    DOI: 10.1007/978-3-642-48016-4_2
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