In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by and .
History
Bochner–Martinelli kernel
For , in the Bochner–Martinelli kernel is a differential form in of bidegree defined by
(where the term is omitted).
Suppose that is a continuously differentiable function on the closure of a domain in n with piecewise smooth boundary . Then the Bochner–Martinelli formula states that if is in the domain then
In particular if is holomorphic the second term vanishes, so
See also
Bergman–Weil formula
Notes
References
. . .
. . . , (ebook). . The first paper where the now called Bochner-Martinelli formula is introduced and proved. . Available at the SEALS Portal . In this paper Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula. . The notes form a course, published by the Accademia Nazionale dei Lincei, held by Martinelli during his stay at the Accademia as "Professore Linceo". . In this article, Martinelli gives another form to the Martinelli–Bochner formula.