# G. V. Lukashenko

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Articles: 1

### About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator

Methods Funct. Anal. Topology 14 (2008), no. 1, 60-66

In the paper, we describe a class of operators $A$ that have empty spectrum and satisfy the nilpotency property of the generated $C_0$-semigroup $U(t)=\exp\{-iAt\},\, t\geqslant 0$, and such that the operator$A^{-1}$ is similar to the integration operator on the corresponding space $L_2(0,a)$.