STRUCTURE OF FACTORS 11 for {w(a)}. Then one concludes r P~ist esf2EvE = f" — Al%xErA'lt dt because ErxEr = el\e-l*a_m + e"\3XEryEr). Then, letting r — + «, one concludes (26). Now, set r e~ist (27) ps(pc) = J " — r Aifxa'ifdt9 x e L($), ß G R. By (22), (25) and (26), we get (28) e^Jn^A + e*)'1*)** = P r fo)), r? G 21', s Å R. For every f G 2Ã, we have /ñ,(ð,(ô?Ì = ^/ 2 ð ((Ä + ^Ã'ô?)*? = ^/2ðé(Á(Ä + â ß Ã1ô?)? = â , / 2 ð à (ßìÄ1 / 2 (Ä + 0" 1 ô? -Éßß ?ðà + e Hence ' ^ t ^ i ^ ^ * by(24) · Therefore, by the uniqueness of the Fourier transform, we conclude /Äßß 7ÃÃ(ß)Ä-,ß/à ? = ð,â-ìÄ"* , / € R. Thus, /Ä!ßç is left bounded for every ç å 31' and ôô,(ÉÁç) Ç = /Ä//ð,.(ô?)Ä-''ß/ ß e R. Setting r = 0, we get /3à C 31 because /£)" = ø, and (29) ð/ (/ô?) = Jnr(n)J, ô ? € 31'. By symmetry, /3l C 31' and (29') ð,Ï/î ) = /*,(?)/", î e 31.
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