X X X X X - Science Reference
X X X X X - Science Reference
X X X X X - Science Reference
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inanopenneighbourhoodoft=0inR.NowsupposethatN=L?1 jL?1andel>0istheG-aryexpansionofN.ThenbyLemma3.6andthetrivialestimate 8el?1 Ps=0eits=el(1+O(t))wehave Xk0aNkeikt=L?1 Xl=0bjl(eit)eitPl?1 MICHAELDRMOTAANDJOHANNESGAJDOSIK<br />
h=0ehel?1 Xs=0eits Pl=0elGjlwithj0>j1>><br />
andthat Nowobservethat=L?1 Xl=0elGjleijlt?jl2t2=2+itPl?1<br />
HenceEeit(XN?N)=N=e?itN=N1NXk0aNkeikt=N e?itN=N=e?it(=)j1=2 itN=it j1=2 0?1+O(j?1 h=0eheO(t+jlt3+(1?)jl)+O(N(1?)): 0(1+O(j?1 0);<br />
=e?t2=2L?1 Xl=0elGjl Neit=(j1=2 0)?Pl?1 h=0eh?(j0?jl)?t2(jl?j0)=(2j0) 0)):<br />
Let">0bea(small)realnumberandletbedenedbyj?1>j0?j"0j.Then j0?j
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