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 (Bergmann 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
- Bergmann, S. (1936), "Über eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen" (in German), Recueil Mathématique (Matematicheskii Sbornik), New Series 1 (43) (6): 851–862, http://mi.mathnet.ru/eng/msb/v43/i6/p851.
- Hazewinkel, Michiel, ed. (2001), "Bergman–Weil representation", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=b/b015570
- Hazewinkel, Michiel, ed. (2001), "Weil domain", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=W/w097610
- Weil, André (1935), "L'intégrale de Cauchy et les fonctions de plusieurs variables", Mathematische Annalen 111 (1): 178–182, doi:10.1007/BF01472212, ISSN 0025-5831.
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