Original scientific paper
Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures
Ivica Nakić
orcid.org/0000-0001-6549-7220
; Department of Mathematics, University of Zagreb, zagreb, Croatia
Abstract
In this paper we present a formula for the calculation of the integrals of the form $\int_S u^{\ast}Xu\,\nu(\deri u)$, where $S$ is the unit sphere in $\mathbb{R}^{N}$, $X$ is a positive semi-definite symmetric matrix, and $\nu$ is a surface measure generated by a Gaussian measure $\mu$. The solution has the form $\mathrm{trace}(XZ)$, with the explicit procedure for the calculation of the matrix $Z$ which does not depend on $X$.
Keywords
integration on a sphere; surface measure
Hrčak ID:
110827
URI
Publication date:
19.11.2013.
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