Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures
Nakić, Ivica
Mathematical Communications, Tome 18 (2013) no. 1, p. 349-358 / Harvested from Mathematical Communications
Text on Mathematical Communications
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 $X$.
Publié le : 2013-11-12
Classification:  
@article{mc329,
     author = {Naki\'c, Ivica},
     title = {Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures},
     journal = {Mathematical Communications},
     volume = {18},
     number = {1},
     year = {2013},
     pages = { 349-358},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc329}
}

Nakić, Ivica. Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures. Mathematical Communications, Tome 18 (2013) no. 1, pp.  349-358. http://gdmltest.u-ga.fr/item/mc329/