Geodesic
Automatic extensions of functional calculi
Studia Mathematica, Tome 114 (1995) no. 3, pp. 237-259 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class, one construction measures how far f(A) is from generating a strongly continuous semigroup, while the other construction measures how far f(A) is from being bounded. We apply our constructions to evolution equations. 
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Ralph deLaubenfels. Automatic extensions of functional calculi. Studia Mathematica, Tome 114 (1995) no. 3, pp. 237-259. doi: 10.4064/sm-114-3-237-259

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