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Polar decomposition of the k-fold product of lebesgue measure on ℝ n

Moghadasi, S. R ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1017/S0004972711003273
  3. Publisher: 2012
  4. Abstract:
  5. The Blaschke-Petkantschin formula is a geometric measure decomposition of the q-fold product of Lebesgue measure on ℝ n. Here we discuss another decomposition called polar decomposition by considering ℝ n× ×ℝ n as n×k and using its polar decomposition. This is a generalisation of the Blaschke-Petkantschin formula and may be useful when one needs to integrate a function g:ℝ n××ℝ n→ℝ with rotational symmetry, that is, for each orthogonal transformation O,g(O(x1),O(xk))=g(x1,xk) . As an application we compute the moments of a Gaussian determinant. Copyright
  6. Keywords:
  7. Blaschke-Petkantschin formula ; Co-area formula ; Moments of Gaussian determinant ; Polar decomposition
  8. Source: Bulletin of the Australian Mathematical Society ; Volume 85, Issue 2 , 2012 , Pages 315-324 ; 00049727 (ISSN)
  9. URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8499631&fileId=S0004972711003273