Mild integrated C-existence families

Shen Wang

Studia Mathematica (1995)

  • Volume: 112, Issue: 3, page 251-266
  • ISSN: 0039-3223

Abstract

top
We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.

How to cite

top

Wang, Shen. "Mild integrated C-existence families." Studia Mathematica 112.3 (1995): 251-266. <http://eudml.org/doc/216152>.

@article{Wang1995,
abstract = {We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.},
author = {Wang, Shen},
journal = {Studia Mathematica},
keywords = { times integrated -existence families without the assumption of exponential boundedness; Hille-Yosida type necessary and sufficient conditions},
language = {eng},
number = {3},
pages = {251-266},
title = {Mild integrated C-existence families},
url = {http://eudml.org/doc/216152},
volume = {112},
year = {1995},
}

TY - JOUR
AU - Wang, Shen
TI - Mild integrated C-existence families
JO - Studia Mathematica
PY - 1995
VL - 112
IS - 3
SP - 251
EP - 266
AB - We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.
LA - eng
KW - times integrated -existence families without the assumption of exponential boundedness; Hille-Yosida type necessary and sufficient conditions
UR - http://eudml.org/doc/216152
ER -

References

top
  1. [1] W. Arendt, Vector valued Laplaced transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352. Zbl0637.44001
  2. [2] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248. 
  3. [3] F. B. Davies and M. M. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. (3) 55 (1987), 181-208. Zbl0651.47026
  4. [4] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985. Zbl0592.47034
  5. [5] M. Hieber and H. Kellerman, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180. Zbl0689.47014
  6. [6] R. deLaubenfels, C-semigroups and the Cauchy problem, J. Funct. Anal., to appear. 
  7. [7] R. deLaubenfels, Integrated semigroups, C-semigroups and the abstract Cauchy problem, Semigroup Forum 41 (1990), 83-95. Zbl0717.47014
  8. [8] R. deLaubenfels, Existence and uniqueness families for the abstract Cauchy problem, J. London Math. Soc. (2) 44 (1991), 310-338. Zbl0766.47011
  9. [9] R. deLaubenfels, C-semigroups and strongly continuous semigroups, Israel J. Math., to appear. Zbl0803.47034
  10. [10] R. deLaubenfels, Automatic well-posedness, preprint. 
  11. [11] I. Miyadera, A generalization of the Hille-Yosida theorem, Proc. Japan Acad. Ser. A 64 (1988), 223-226. Zbl0683.47027
  12. [12] I. Miyadera and N. Tanaka, Exponentially bounded C-semigroups and generation of semigroups, J. Math. Anal. Appl. 143 (1989), 358-378. Zbl0697.47039
  13. [13] I. Miyadera and N. Tanaka, Exponentially bounded C-semigroups and integrated semigroups, Tokyo J. Math. 12 (1989), 99-115. Zbl0702.47028
  14. [14] F. Neubrander, Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math. 135 (1988), 111-157. Zbl0675.47030
  15. [15] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. 
  16. [16] N. Tanaka, On the exponentially bounded C-semigroups, Tokyo J. Math. 10 (1987), 107-117. Zbl0631.47029
  17. [17] H. R. Thieme, "Integrated semigroups" and integrated solutions to abstract Cauchy problems, J. Math. Anal. Appl. 152 (1990), 416-447. Zbl0738.47037

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.