A residue formula for integrals with hyperplane singularities
Andrew O'Desky
TL;DR
This paper introduces a novel residue formula for evaluating integrals with singularities on affine hyperplanes, utilizing a stability concept for real matrices inspired by total positivity.
Contribution
It presents a new residue formula specifically designed for integrals with hyperplane singularities, incorporating a stability notion for real matrices.
Findings
Derived a residue formula for hyperplane singularities
Introduced a stability concept for real matrices
Connected stability with total positivity principles
Abstract
We prove a new residue formula for integrals with singularities along affine hyperplanes. Our formula makes use of a notion for real matrices called stability which is inspired by ideas from total positivity.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical functions and polynomials · Advanced Banach Space Theory