id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
easat-2091	Osman, Osman Abdalla Adam 	Factors affecting mobility of harmonic symbols	2024	7	.pdf	application/pdf	4175	194	78	𝑓2(0)̅̅ ̅̅ ̅̅ ̅g2(0)̅̅ ̅̅ ̅̅ ̅ = 〈𝑇𝜑 + 1𝑇𝜓 + 11,1〉 = 〈𝑓1g1 + g2(0)̅̅ ̅̅ ̅̅ ̅𝑓1 + 𝑓2̅g1 + 𝑓2(0)̅̅ ̅̅ ̅̅ ̅g2(0)̅̅ ̅̅ ̅̅ ̅, 1〉 = ∫𝐷(𝑓1g1 + g2(0)̅̅ ̅̅ ̅̅ ̅𝑓1 + 𝑓2̅g1 + 𝑓2(0)̅̅ ̅̅ ̅̅ ̅g2(0)̅̅ ̅̅ ̅̅ ̅)𝑑𝐴 = 𝜋[𝑓2(0)g1(0) + 𝑓1(0)g2(0)̅̅ ̅̅ ̅̅ ̅ + 𝑓2(0)̅̅ ̅̅ ̅̅ ̅g2(0)̅̅ ̅̅ ̅̅ ̅] + ∫𝐷𝑓2̅g1𝑑𝐴 (10) So that 𝑇𝜑 + 1𝑇𝜑 + 1̅̅ ̅̅ ̅̅ ̅̅ = 𝑇𝜑 + 1̅̅ ̅̅ ̅̅ ̅̅ 𝑇𝜑 + 1 and so Theorem 1 implies that (𝜑 + 1) and (𝜑 + 1̅̅ ̅̅ ̅̅ ̅̅ ̅) are both analytic on 𝐷 (in which case (𝜑 + 1) is constant, so we are done) or there are Constants𝛼, 𝛽 ∈ 𝐶, not both 0, such that 𝑎(𝜑 + 1) + 𝑏(𝜑 + 1̅̅ ̅̅ ̅̅ ̅̅ ̅) (𝜑 + 1) is constant on 𝐷.	cache/easat-2091.pdf	txt/easat-2091.txt