Displaying similar documents to “Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators.”

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of A n , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...

Automatic extensions of functional calculi

Ralph deLaubenfels (1995)

Studia Mathematica

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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,...

On analytic semigroups and cosine functions in Banach spaces

V. Keyantuo, P. Vieten (1998)

Studia Mathematica

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform. ...