Regularization of semigroups that are strongly continuous for $t>0$
HTML articles powered by AMS MathViewer
- by P. C. Kunstmann PDF
- Proc. Amer. Math. Soc. 126 (1998), 2721-2724 Request permission
Abstract:
Let $E$ be a Banach space and $T:]0,\infty [\to L(E)$ a strongly continuous semigroup with $\bigcap _{t>0}\operatorname {Kern} T_t=\{0\}$. We show that the generator $A$ of $(T_t)$ generates a regularized semigroup. Our construction of a regularizing operator uses an existence result of J. Esterle.References
- G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223–248 (Italian). MR 225199
- E. B. Davies and M. M. H. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. (3) 55 (1987), no. 1, 181–208. MR 887288, DOI 10.1112/plms/s3-55.1.181
- Ralph deLaubenfels, Existence families, functional calculi and evolution equations, Lecture Notes in Mathematics, vol. 1570, Springer-Verlag, Berlin, 1994. MR 1290783, DOI 10.1007/BFb0073401
- J. Esterle, Elements for a classification of commutative radical Banach algebras, Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981), Lecture Notes in Math., vol. 975, Springer, Berlin-New York, 1983, pp. 4–65. MR 697578
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- P.C. Kunstmann, A new class of regularizable strongly continuous semigroups of fast growth near the origin, submitted.
- Isao Miyadera and Naoki Tanaka, Exponentially bounded $C$-semigroups and generation of semigroups, J. Math. Anal. Appl. 143 (1989), no. 2, 358–378. MR 1022541, DOI 10.1016/0022-247X(89)90046-2
- Shinnosuke Ôharu, Semigroups of linear operators in a Banach space, Publ. Res. Inst. Math. Sci. 7 (1971/72), 205–260. MR 0312323, DOI 10.2977/prims/1195193542
- Naoki Tanaka and Isao Miyadera, $C$-semigroups and the abstract Cauchy problem, J. Math. Anal. Appl. 170 (1992), no. 1, 196–206. MR 1184734, DOI 10.1016/0022-247X(92)90013-4
Additional Information
- P. C. Kunstmann
- Affiliation: Mathematisches Seminar der Universität Kiel, Ludewig-Meyn-Straße 4, D–24098 Kiel, Germany
- Address at time of publication: Mathematisches Institut I der Universität Karlsruhe, Englerstraße 2, Postfach 6980, D–76128 Karlsruhe, Germany
- Email: peer.kunstmann@math.uni-karlsruhe.de
- Received by editor(s): February 7, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2721-2724
- MSC (1991): Primary 47D03, 47D06
- DOI: https://doi.org/10.1090/S0002-9939-98-04636-X
- MathSciNet review: 1473671