Ghaani Farashahi, A. (2017). Trigonometric polynomials over homogeneous spaces of compact groups. Advances in Operator Theory, 2(1), 87-97. doi: 10.22034/aot.1701-1090
Arash Ghaani Farashahi. "Trigonometric polynomials over homogeneous spaces of compact groups". Advances in Operator Theory, 2, 1, 2017, 87-97. doi: 10.22034/aot.1701-1090
Ghaani Farashahi, A. (2017). 'Trigonometric polynomials over homogeneous spaces of compact groups', Advances in Operator Theory, 2(1), pp. 87-97. doi: 10.22034/aot.1701-1090
Ghaani Farashahi, A. Trigonometric polynomials over homogeneous spaces of compact groups. Advances in Operator Theory, 2017; 2(1): 87-97. doi: 10.22034/aot.1701-1090
Trigonometric polynomials over homogeneous spaces of compact groups
This paper presents a systematic study for trigonometric polynomials over homogeneous spaces of compact groups. Let $H$ be a closed subgroup of a compact group $G$. Using the abstract notion of dual space $\widehat{G/H}$, we introduce the space of trigonometric polynomials $\mathrm{Trig}(G/H)$ over the compact homogeneous space $G/H$. As an application for harmonic analysis of trigonometric polynomials, we prove that the abstract dual space of any homogeneous space of compact groups separates points of the homogeneous space in some sense.