Bergman–Weil formula
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In mathematics, the Bergman–Weil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by Bergman (1936) and Weil (1935).
Weil domains
A Weil domain (Weil 1935) is an analytic polyhedron with a domain U in Cn defined by inequalities fj(z) < 1 for functions fj that are holomorphic on some neighborhood of the closure of U, such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2n − 1, and the intersections of k faces have codimension at least k.
See also
References
- Bergman, S. (1936), "Über eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen", Rec. Math. (Mat. Sbornik) N.S., 1(43) (6): 851–862
- Chirka, E.M. (2001), "b/b015570", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Shirinbekov, M. (2001), "Weil domain", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Weil, André (1935), "L'intégrale de Cauchy et les fonctions de plusieurs variables", Mathematische Annalen (Springer Berlin / Heidelberg) 111: 178–182, doi:10.1007/BF01472212, ISSN 0025-5831
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