Strongly continuous integrated C-cosine operator functions
Wang, Shen ; Huang, Zhen
Studia Mathematica, Tome 122 (1997), p. 273-289 / Harvested from The Polish Digital Mathematics Library

We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP2) are also presented.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216455
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     author = {Shen Wang and Zhen Huang},
     title = {Strongly continuous integrated C-cosine operator functions},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {273-289},
     zbl = {0908.47040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv126i3p273bwm}
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Wang, Shen; Huang, Zhen. Strongly continuous integrated C-cosine operator functions. Studia Mathematica, Tome 122 (1997) pp. 273-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv126i3p273bwm/

[00000] [A] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352. | Zbl 0637.44001

[00001] [D] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248.

[00002] [Dav-P] E. B. Davies and M. M. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181-208. | Zbl 0651.47026

[00003] [deL] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994. | Zbl 0811.47034

[00004] [del-P] R. deLaubenfels and S. Piskarev, Growth rate of cosine families, J. Math. Anal. Appl. 196 (1995), 442-451. | Zbl 0844.34061

[00005] [L-S1] Y.-C. Li and S.-Y. Shaw, On generators of integrated C-semigroups and C-cosine functions, Semigroup Forum 47 (1993), 29-35.

[00006] [L-S2] Y.-C. Li and S.-Y. Shaw, Integrated C-cosine functions and the abstract Cauchy problem, preprint.

[00007] [S-L1] S.-Y. Shaw and Y.-C. Li, On N-times integrated C-cosine functions, in: Evolution Equations, Marcel Dekker, New York, 1994, 393-406. | Zbl 0935.47032

[00008] [S-L2] S.-Y. Shaw and Y.-C. Li, N-times integrated C-semigroups and the abstract Cauchy problem, Taiwanese J. Math. 1 (1997), 75-102. | Zbl 0892.47042

[00009] [So] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.

[00010] [W-Wa] H. Wang and S. Wang, C-cosine operator functions and the applications to the second order abstract Cauchy problem, in: Functional Analysis in China, Kluwer Acad. Publ., Dordrecht, 1996, 333-350. | Zbl 0908.47039

[00011] [Wa] S. Wang, Mild integrated C-existence families, Studia Math. 112 (1995), 251-266. | Zbl 0819.47054