Supplement to F. Wiener sieve theorem

• Date: 2015
• Main Authors: Savchuk, V. V., Chaichenko, S. O., Савчук, В. В., Чайченко, С. О.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2015
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/301
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

The theorem of F. Wiener about sieve states: the norm of the operator $\mathcal W_{r,s} : f(z)=\sum_{j=0}^\infty \widehat f_jz^j\mapsto \sum_{j=0}^\infty \widehat f_{js+r}z^j$ on the space of bounded holomorphic in the disk $\mathbb D=\{z : |z|<1\}$ functions is 1 if $r<s$. We...