Polar Integral

Authors

  • S. Reza Moghadasi

Keywords:

Blaschke-Petkantschin formula, Coarea formula, Polar decomposition, Moments of Gaussian determinant.

Abstract

Blaschke-Petkantschin formula is a geometric measure decomposition of the q-fold product of Lebesgue measure of $\R^n$. Here we discus another decomposition called polar decomposition by considering $\R^n \times \dots \R^n$ as $\mnk$ and using its polar decomposition. It is a generalization of Blaschke-Petkantschin formula and may be useful when one needs to integrate a function $g:\R^n \times \dots \times \R^n \to \R$ with rotational symmetry i.e. for each $O \in \on$, $g(O(x_1), \dots , O(x_k)) = g(x_1, \dots x_k)$. As an application we compute the moments of Gaussian determinant. DOI: 10.1017/S0004972711003273

Published

2012-02-27

Issue

Vol. 85 No. 2 (2012)

Section

Articles
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