Strongly continuous integrated C-cosine operator functions

• Autorzy: Shen Wang Wang , Zhen You Huang
• Języki publikacji: EN

Abstrakty

EN

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 (ACP$_2$) are also presented.

Kategorie tematyczne

• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 126
• Numer: 3
• Strony: 273-289

Daty

wydano

1997

otrzymano

1996-12-09

poprawiono

1997-05-21

Twórcy

autor

Shen Wang Wang

• Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

autor

Zhen You Huang

• Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

Bibliografia

• [A] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
• [D] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248.
• [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.
• [deL] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994.
• [del-P] R. deLaubenfels and S. Piskarev, Growth rate of cosine families, J. Math. Anal. Appl. 196 (1995), 442-451.
• [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.
• [L-S2] Y.-C. Li and S.-Y. Shaw, Integrated C-cosine functions and the abstract Cauchy problem, preprint.
• [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.
• [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.
• [So] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.
• [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.
• [Wa] S. Wang, Mild integrated C-existence families, Studia Math. 112 (1995), 251-266.