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Published online by Cambridge University Press: 08 January 2025
In this paper, we study the embedding problem of an operator into a strongly continous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space  $H^2$. In particular, we focus on the isometric ones using the necessary and sufficient condition observed by T. Eisner.
$H^2$. In particular, we focus on the isometric ones using the necessary and sufficient condition observed by T. Eisner.
 ${H}^2$
. Houston J. Math. 30(2004), no. 1, 137–145.Google Scholar
${H}^2$
. Houston J. Math. 30(2004), no. 1, 137–145.Google Scholar