Geodesic
Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 47-53

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DOI

We prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold: for any x ∊ D(A n ) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T. G. Kurtz [3]. Similar inequalities are proved for cosine operator funtions.
DOI : 10.4153/CMB-1989-007-x
Mots-clés : Norm inequalities, analytic semigroup of operators, infinitesimal generator, cosine operator function 
Siddiqi, Jamil A.; Elkoutri, Abdelkader. Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 47-53. doi: 10.4153/CMB-1989-007-x
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     title = {Norm {Inequalities} for {Generators} of {Analytic} {Semigroups} and {Cosine} {Operator} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {47--53},
     year = {1989},
     volume = {32},
     number = {1},
     doi = {10.4153/CMB-1989-007-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-007-x/}
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