Titlebook: Vector-valued Laplace Transforms and Cauchy Problems; Wolfgang Arendt,Charles J. K. Batty,Frank Neubrand Book 20011st edition Birkhäuser B

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Vector-valued Laplace Transforms and Cauchy Problems

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Wolfgang Arendt,Charles J. K. Batty,Frank Neubrand

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Cauchy Problemsn Laplace transforms from Section 1.7. Much attention is given to holomorphic semigroups which are particularly simple to characterize by means of the results of Section 2.6. We consider not only holomorphic semigroups which are strongly continuous at 0, but more general holomorphic semigroups which

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Translation Invariant Operators On ,,(ℝ,)gument are our main tools. Proposition 8.2.3 gives a simple criterion for a function to belong to the Fourier algebra ..(ℝ.) and hence to be a Fourier multiplier on ..(ℝ.). These techniques are essential for our main results.

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