Tag

integral formulas

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 classical Cauchy integral formula and its smooth counterpart, whose extra volume term measures the failure of holomorphicity.

mathematics

mathematicscomplex analysisintegral formulas

The Cauchy Integral Formula Beyond Analyticity

What survives of the Cauchy integral formula when the function is no longer analytical? A smooth version exists, and a single volume term measures exactly how far holomorphicity fails.

October 2, 20251 min read