Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Automatic extensions of local regularized semigroups and local regularized cosine functions

Author(s): Sheng Wang Wang; Ming Chu Gao
Journal: Proc. Amer. Math. Soc. 127 (1999), 1651-1663.
MSC (1991): Primary 47D05, 47F05
Posted: February 16, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: This paper establishes automatic extensions for local regularized semigroups and local regularized cosine functions in a certain sense and applies the results to abstract Cauchy problems.


References:

[A-El-K]
W. Arendt, O. El-Mennaoui and V. Keyantuo, Local Integrated Semigroups: Evolution with jumps of Regularity, J. Math. Anal. Appl. 186 (1994,), 572-595. MR 95f:47065

[dL 1]
R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math., Springer-Verlag, 1570, 1994. MR 96b:47047

[dL 2]
R. deLaubenfels, Existence and Uniqueness Families for the abstract Cauchy problem, J. London Math. Soc. 44 (1991), 310-338. MR 92k:34075

[dL 3-S-Wa]
R. deLaubenfels, G. Sun and S. W. Wang, Regularized Semigroups, Existence Families and the abstract Cauchy problem, Diff. Int. Eq. 8 (1995), 1477-1496. MR 96j:47035

[dL 4-Wa]
R. deLaubenfels, S. W. Wang, Spectral Conditions guaranteeing a Non-trivial Solution of the abstract Cauchy problem, Proc. Amer. Math. Soc., to appear.

[dL 5]
R. deLaubenfels, Automatic extensions of functional calculi, Studia Math. 114 (1995), 237-259. MR 96f:47029

[F]
H. O. Fattorini, Existence and behavior at infinity of solutions of certain linear operational differential equations, Pacific J. Math. 33 (1970), 583-615. MR 41:8789

[G]
M. C. Gao, Local C-semigroups and Local C-cosine functions, preprint.

[H-Hu]
F. Huang, T. Huang, Local C-cosine family theory and application, Chinese Ann. Math. Ser. 16B (1995), 213-232. MR 96g:47040

[L]
J. L. Lions, Les Semi-groupes Distributions, Portugal. Math. 19 (1960), 141-164. MR 26:611

[S]
G. Sun, Integrated C-semigroups, Local C-semigroups, Mild C-existence families and (ACP), Dissertation (Chinese).

[T-O]
N. Tanaka, N. Okazawa, Local C-Semigroups and Local Integrated Semigroups, Proc. London Math. Soc. 61 (1990), 63-90. MR 91b:47093

[W-Wa]
H. Wang, S. W. Wang, C-Cosine Operator Functions and the Applications to the Second Order Abstract Cauchy Problem, Functional Analysis in China, Kluwer Acad. Publ. (Netherlands) 1996.

[Wa 1]
S. W. Wang, Quasi-distribution Semigroups and Integrated Semigroups, J. Funct. Anal. 146 (1997), 352-381. MR 98d:47088

[Wa 2]
S. W. Wang, Strongly Continuous Groups and Semigroups of Generalized Scalar Operators, submitted.


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D05, 47F05

Retrieve articles in all Journals with MSC (1991): 47D05, 47F05


Additional Information:

Sheng Wang Wang
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People's Republic of China
Address at time of publication: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859
Email: wang2598@netra.nju.edu.cn

Ming Chu Gao
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People's Republic of China
Address at time of publication: Department of Mathematics, Shanxi Teachers University, Linfen, Shanxi 041000, People's Republic of China

DOI: 10.1090/S0002-9939-99-04859-5
PII: S 0002-9939(99)04859-5
Received by editor(s): May 1, 1997
Posted: February 16, 1999
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google