The Hille-Yosida theorem for local convoluted semigroups

Proceedings of the Edinburgh Mathematical Society

Volumn 46, Issue 2, 2003, Pages 395-413

  Keyantuo, Valentin ^a   Müller, Claus ^b   Vieten, Peter ^b  

^a UNIVERSITY OF PUERTO RICO   (Puerto Rico)

^b University of Koblenz Landau   (Germany)

Author keywords

Distribution semigroup; Integrated semigroup; Local convoluted semigroup; Local Laplace transform; Ultradistribution semigroup

Indexed keywords

EID: 0041913050     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0013091500001103     Document Type: Conference Paper

References (18)

1. W. ARENDT, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
2. W. ARENDT, O. EL-MENNAOUI AND V. KEYANTUO, Local integrated semigroups: evolution with jumps of regularity, J. Math. Analysis Applic. 186 (1994), 572-595.
3. W. ARENDT, C. J. K. BATTY, M. HIEBER AND F. NEUBRANDER, Vector-valued Laplace transforms and Cauchy problems, Monographs in Mathematics, vol. 96 (Birkhäuser, 2001).
4. B. BÄUMER AND F. NEUBRANDER, Laplace transform methods for evolution equations. Conf. Semin. Mat. Univ. Bari 259 (1994), 27-60.
5. J. CHAZARAIN. Problèmes de Cauchy abstraits et application à quelques problèmes mixtes, J. Funct. Analysis 7 (1971), 386-446.
6. I. CIORANESCU, Local convoluted semigroups, Lecture Notes in Pure and Applied Mathematics, no. 168, pp. 107-122 (Marcel Dekker, New York, 1995).
7. I. CIORANESCU AND G. LUMER, Problèmes d'évolution régularisés par un noyau général K(t), Formule de Duhamel, prolongement, théorèmes de génération. C. R. Acad. Sci. Paris Sér. I 319 (1994), 1273-1278.
8. I. CIORANESCU AND G. LUMER, On K (t)-convoluted semigroups, Pitman Research Notes in Mathematics, vol. 324, pp. 86-93 (1995).
9. G. DOETSCH, Handbuch der Laplace transformation, vol. 1 (Birkhäuser, 1971).
10. N)-spaces, Math. Ann. 291 (1991), 1-16.
11. V. KEYANTUO, C. MÜLLER AND P. VIETEN, The finite and local Laplace transforms in Banach spaces, Proc. Edinb. Math. Soc. 46 (2003), 357-372.
12. S. KREIN, Linear differential equations in Banach space, American Mathematical Society Translations of Mathematical Monographs (1971).
13. J. L. LIONS, Les semigroupes distributions, Portugaliae Math. 19 (1960), 141-164.
14. F. NEUBRANDER, Integrated semigroups and their applications to the abstract Cauchy problem, Pac. J. Math. 135 (1989), 233-251.
15. A. PAZY, Semigroups of linear operators and applications to partial differential equations (Springer, 1983).
16. N. TANAKA AND N. OKAZAWA, Local C-semigroups and local integrated semigroups, Proc. Land. Math. Soc. 61 (1990), 63-90.
17. H. R. THIEME, Integrated semigroups and integrated solutions to the abstract Cauchy problem, J. Math. Analysis Applic. 152 (1990), 416-447.
18. D. V. WIDDER, The Laplace transform (Princeton University Press, Princeton, NJ, 1946).