Bochner–Martinelli formula

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.