Lema 1 Wirsing
Posted: Mon Nov 17, 2008 10:16 am
Fiind dat \( \epsilon>0 \), sa se arate ca exista o functie continua \( \sigma \) astfel incat
\( \xi\sigma(\xi)=\int_0^{\xi}\sigma(\xi-\eta)d\sigma(\eta)+O(\log\xi), \xi\geq 2 \),
iar daca \( \sigma^{\prime} \) este derivata lui \( \sigma \), atunci
\( |\sigma^{\prime}(\xi)|\leq 1+\epsilon, \)
pentru \( \xi>0 \), execeptand o multime numarabila de puncte \( \xi=\xi_{n} \), \( n=1,2, \ldots, n \).
\( \xi\sigma(\xi)=\int_0^{\xi}\sigma(\xi-\eta)d\sigma(\eta)+O(\log\xi), \xi\geq 2 \),
iar daca \( \sigma^{\prime} \) este derivata lui \( \sigma \), atunci
\( |\sigma^{\prime}(\xi)|\leq 1+\epsilon, \)
pentru \( \xi>0 \), execeptand o multime numarabila de puncte \( \xi=\xi_{n} \), \( n=1,2, \ldots, n \).