Convergence of operator Riemann sums

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76 5 A-L-G interpolation means M

when for example 0 2 . Hence, as usual we have lim0 , 0, 2 0 and so lim0 , 0, 1 0. Consequently lim M (H, K)X M0 (H, K)X 0. 0

 Now, consider the case     0. We have

   M (ex , 1)     (1  )    sinh 2 x   sinh 1
                                                  2 x
                                                  , (x)
   M (ex , 1)   ()(1  )    sinh 2 x   sinh 1
                                                  2 x

for some positive , L1 (R). Since the estimate ...

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