Representations of a Group of Linear Operators in a Banach Space on the Set of Entire Vectors of its Generator

• Date: 2015
• Main Authors: Gorbachuk, V. M., Gorbachuk, M. L., Горбачук, В. М., Горбачук, М. Л.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2007
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For a strongly continuous one-parameter group $\{U(t)\} t ∈(−∞,∞)$ of linear operators in a Banach space $\mathfrak{B}$ with generator $A$, we prove the existence of a set $\mathfrak{B}_1$ dense in $\mathfrak{B}_1$ on the elements $x$ of which the function $U(t)x$ admits an extension to an entire B$...