Tag

several complex variables

2 posts

mathematicscomplex analysisseveral complex variables+1 more

The Bochner–Martinelli Formula

Closing the cycle on the Cauchy integral formula: Bochner–Martinelli recovers a function from its boundary data, up to a term measuring the failure of holomorphicity, with one universal kernel.

October 25, 20252 min read

The Cauchy–Leray–Fantappiè theorem: a kernel of type (n, n-1) assembled from a defining function of the boundary, and the reproducing formula it yields on a bounded domain in C^n.

mathematics

mathematicscomplex analysisseveral complex variables

The Cauchy–Leray–Fantappiè Formula in Several Variables

In several complex variables there is no translation-invariant holomorphic kernel. The Cauchy–Leray–Fantappiè formula answers this by building its kernel from a defining function of the boundary.

October 18, 20251 min read