Geodesic
A direct approach to the Weiss conjecture for bounded analytic semigroups
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 527-539.

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We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded $H^{\infty }$-calculus and is based on elementary analysis.
Classification : 34K35, 35F50, 35Q93, 47D06, 93B28, 93B36
Keywords: infinite dimensional systems; analytic semigroups; unbounded observation operator; admissibility; fractional power 
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     author = {Hamid, Bounit and Adberrahim, Driouich and Omar, El-Mennaoui},
     title = {A direct approach to the {Weiss} conjecture for bounded analytic semigroups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {527--539},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {2010},
     mrnumber = {2657967},
     zbl = {1220.47058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a17/}
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Hamid, Bounit; Adberrahim, Driouich; Omar, El-Mennaoui. A direct approach to the Weiss conjecture for bounded analytic semigroups. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 527-539. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a17/