On the relation between the semigroup and its infinitesimal generator
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- by Frank Neubrander PDF
- Proc. Amer. Math. Soc. 100 (1987), 104-108 Request permission
Abstract:
We prove that for a semigroup generator $A$ the solutions of $u’(t) = Au(t)$ and $u(0) = x$ are completely determined by the resolvent of $A$ along an equidistant sequence ${({s_0} + nr)_{n \in {\mathbf {N}}}},r \in {\mathbf {R}},{s_0} \in {\mathbf {C}}$, of points in the resolvent set of $A$.References
- Edward Brian Davies, One-parameter semigroups, London Mathematical Society Monographs, vol. 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 591851
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373 F. Neubrander, Well-posedness of higher order abstract Cauchy problems, Dissertation, Tuebingen, 1984.
- Frank Neubrander, Laplace transform and asymptotic behavior of strongly continuous semigroups, Houston J. Math. 12 (1986), no. 4, 549–561. MR 873650
- E. Phragmén, Sur une extension d’un théorème classique de la théorie des fonctions, Acta Math. 28 (1904), no. 1, 351–368 (French). MR 1555006, DOI 10.1007/BF02418391
- David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
- Kôsaku Yosida, Functional analysis, 5th ed., Grundlehren der Mathematischen Wissenschaften, Band 123, Springer-Verlag, Berlin-New York, 1978. MR 0500055
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 104-108
- MSC: Primary 47D05; Secondary 44A10
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883409-5
- MathSciNet review: 883409