Cayley transform of the generator of a uniformly bounded $C_0$-semigroup of operators

• Date: 2004
• Main Authors: Gomilko, A. M., Гомилко, А. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3819
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the problem of estimates for the powers of the Cayley transform $V = (А + I)(А - I)^{-1}$ of the generator of a uniformly bounded $C_0$-semigroup of operators $e^{tA} , t \geq 0$, that acts in a Hilbert space $H$. In particular, we establish the estimate $\sup_{n \in N}\left(||V^n||/\ln...