Bio Norm continuity in parameter

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92 7 Binomial means B

have B M because the binomial expansion is available. We also recall M1/2 B for 0 ([39, Proposition 3.3]) so that we observe () () B B M1/2 M1/2 M

(see ()). Therefore, in the rest of the proof we may and do assume 0 and n1 (n 1, 2, ), and it suces to see that the function (t) (see (7.2)) is positive denite. Recall that the Fourier transform of eax (with a 0) is 2a(x2 a2 )1 :

                                       a        1         2a
                 eay eixy dy  2   2            2                 (7.3)
                                     ...

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