id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-4612	Celeghini, Enrico; Gadella, Manuel; del Olmo, Mariano A	LIE ALGEBRA REPRESENTATIONS AND RIGGED HILBERT SPACES: THE SO(2) CASE	2017	6	.pdf	application/pdf	3903	219	73	Since this theorem is only valid for |f〉, |g〉 ∈ Φ, we conclude that (12) is only valid for |f〉 ∈ Φ from a strictly rigorous point of view. Since R(θ) is unitary on L2[0, 2π] for any value of θ then R(θ) is also unitary on H due to the unitarity of S. Unitary operators leaving Φ invariant can be ex- tended to Φ× by the duality formula (1), i.e., 〈R(θ)F |f〉 = 〈F |R(−θ)f〉, ∀ |f〉 ∈ Φ, ∀F ∈ Φ×. Therefore, 〈R(θ)φ|f〉	cache/ap-4612.pdf	txt/ap-4612.txt