# Strongly continuous integrated C-cosine operator functions

Studia Mathematica (1997)

- Volume: 126, Issue: 3, page 273-289
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topWang, Shen, and Huang, Zhen. "Strongly continuous integrated C-cosine operator functions." Studia Mathematica 126.3 (1997): 273-289. <http://eudml.org/doc/216455>.

@article{Wang1997,

abstract = {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.},

author = {Wang, Shen, Huang, Zhen},

journal = {Studia Mathematica},

keywords = {regularized semigroups; strongly continuous -times integrated -cosine operator functions; abstract Cauchy problem},

language = {eng},

number = {3},

pages = {273-289},

title = {Strongly continuous integrated C-cosine operator functions},

url = {http://eudml.org/doc/216455},

volume = {126},

year = {1997},

}

TY - JOUR

AU - Wang, Shen

AU - Huang, Zhen

TI - Strongly continuous integrated C-cosine operator functions

JO - Studia Mathematica

PY - 1997

VL - 126

IS - 3

SP - 273

EP - 289

AB - 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.

LA - eng

KW - regularized semigroups; strongly continuous -times integrated -cosine operator functions; abstract Cauchy problem

UR - http://eudml.org/doc/216455

ER -

## References

top- [A] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352. Zbl0637.44001
- [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. Zbl0651.47026
- [deL] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994. Zbl0811.47034
- [del-P] R. deLaubenfels and S. Piskarev, Growth rate of cosine families, J. Math. Anal. Appl. 196 (1995), 442-451. Zbl0844.34061
- [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. Zbl0935.47032
- [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. Zbl0892.47042
- [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. Zbl0908.47039
- [Wa] S. Wang, Mild integrated C-existence families, Studia Math. 112 (1995), 251-266. Zbl0819.47054

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.