# Mathematical Communications,Vol. 18 No. 2, 2013

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

 Fulltext: english, pdf (131 KB) pages 349-358 downloads: 252* cite APA 6th EditionNakić, I. (2013). Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures. Mathematical Communications, 18 (2), 349-358. Retrieved from https://hrcak.srce.hr/110827 MLA 8th EditionNakić, Ivica. "Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures." Mathematical Communications, vol. 18, no. 2, 2013, pp. 349-358. https://hrcak.srce.hr/110827. Accessed 15 Apr. 2021. Chicago 17th EditionNakić, Ivica. "Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures." Mathematical Communications 18, no. 2 (2013): 349-358. https://hrcak.srce.hr/110827 HarvardNakić, I. (2013). 'Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures', Mathematical Communications, 18(2), pp. 349-358. Available at: https://hrcak.srce.hr/110827 (Accessed 15 April 2021) VancouverNakić I. Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures. Mathematical Communications [Internet]. 2013 [cited 2021 April 15];18(2):349-358. Available from: https://hrcak.srce.hr/110827 IEEEI. Nakić, "Integration of positive linear functionals on a sphere in $R^{2n}$ with respect to Gaussian surface measures", Mathematical Communications, vol.18, no. 2, pp. 349-358, 2013. [Online]. Available: https://hrcak.srce.hr/110827. [Accessed: 15 April 2021]

Abstracts
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 $X$.

Hrčak ID: 110827

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