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By EDMUND LANDAU

ISBN-10: 3642900127

ISBN-13: 9783642900129

ISBN-10: 3642918697

ISBN-13: 9783642918698

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Extra info for Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie

Sample text

1 f 'lt h (m) -(1 T -'It cp sin cP 2 (J cos cP + (2)2 cl m -~ 0 T zu zeigen. Bei jedem emit 0 < c < n; ist fiir - n; < cp < - c und fUr c < cp < n; 1 - 21? cos cP + 1;'2 :> 1 - 21? cos c + (J2 also der Integrand filr 0 < Daher ist Q< = (Q - cos 8 y+ sin2 c :> sin2 8, 1 als Funktion von Q, cp beschrankt. [If'lt ~cp sin cP I (llim/1- Q) I _}(cp) (1~-=-1rQcos cp-+Qi)" clcp, _- -. IfE h(cp)-(l hm (1-1;')1 (I = 1 -E ~--- < Max. ) ICP

If'lt ~cp sin cP I (llim/1- Q) I _}(cp) (1~-=-1rQcos cp-+Qi)" clcp, _- -. IfE h(cp)-(l hm (1-1;')1 (I = 1 -E ~--- < Max. ) ICP- 0 gibt die Behauptung. - 43 - Zweites Kapitel. Summabilitat hoherer Ordnung. § 6. Der Knopp-Schneesche Satz. Hilfssatz 1. Voraussetzung: Es sei Xu X 2 , GraBen, q:> 0 ganz ~~nd bei n __ 00 Xn ••• , ...

In ( " Wegen = g{recpt) ecpi i"f(Recpt)dR o existiert nach V oraussetzung ffir -" -< qJ -< " lim 9 (re91 t) 1'=1 = G(cp) gleichmaBig in qJ, ist also stetig, und fiir 0 -< Q -< 1 ist daher In G( ) sin qJ d 1) f( ) = - i (1 - ~2) ~ " - n qJ (1- 2(> cos qJ + ,l)! rp, Fiir 0 -< r -< 1, a -< qJ -< P ist nach V oraussetzung If(re91 i ) I -< P. G(qJ) hat daher fiir a -< qJ -< P beschrankten Differenzenquotienten; denn fiir a -< qJl -< qJa -< p, 0 -< r -< 1 ist Ig (re91a t) - 9 (re911 t) I = r I~~a f{re 91t) e91 i d qJ I-< P(qJ2 - qJl)' ,· a = -< qJl -< qJ2 -

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Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie by EDMUND LANDAU


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