id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-1017	Aswhad, A. A.	On the Riesz Means of Expansion by Riesz Bases Formed by Eigen Functions for the Ordinary Differential Operator of 2mth Order	2017	9	.pdf	application/pdf	3596	114	80	SC I. VO L.23 (2) 2010 From L 1(G) into C(K) for any compact KG we know that r 2 s sr r r 2 (f, x) f, v u (x)(1 )          s s r r R r S (f ,x) f , v u , W     Then s s s s s s R r r R r (f, x) S (f , x) f, W f, v u , W           …(9) Holds uniformly on the compact interval KG. For the proof of this theorem we shall choose the 2m-th roots r,i (i=1,2,…,2m) of r such that Re r,1  Re r,2… Re r,m 0 Re r,m+1 … Re r,2m and put r = r,m, r=Re r, r=Im r . Now, we have from ([3]) r r r r r r r 1 r 1 r 1 r 2 r 2 r 2 r m r m r m r ˆ ˆ ˆ ˆ ˆ ˆ ˆu (x) u (x t) u (x t) u (x 2R) u (x 2R)	cache/iajs-1017.pdf	txt/iajs-1017.txt