Regularized semigroups and systems of linear partial differential equations

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1. [Ar1] W. Arendt, Vector valued Laplace transforms and Cauchy problems, Israel J. Math.59 (1987), 327-352. Zbl0637.44001MR920499
2. [Ar2] W. Arendt, Sobolev imbeddings and integrated semigroups, in: Semigroup theory and Evolution. Ph. Clément, E. Mitidieri, B. de Pagter, (eds.). Lecture Notes in Pure and Appl. Math., Marcel Dekker, 135, (1991), 29-40. Zbl0762.47013MR1164640
3. [A-K] W. Arendt - H. Kellermann, Integrated solutions of Volterra integro-differential equations and applications, in: Volterra Integrodifferential Equations in Banach Spaces and Applications. G. Da Prato, M. Iannelli (eds.). Pitman, 190, (1989), 21-51. Zbl0675.45017MR1018871
4. [A-N-S] W. Arendt - F. Neubrander - U. Schlotterbeck, Interpolation of semigroups and integrated semigroups, Semigroup Forum, 45, n. 1, (1992), 26-37. Zbl0782.47035MR1161416
5. [DaP1] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat.15 (1966), 223-246. Zbl0195.41001MR225199
6. [DaP2] G. Da Prato, Semigruppi di crescenza n, Ann. Scuola Norm. Sup. Pisa Cl. Sci.20 (1966), 753-782. Zbl0198.16801MR222710
7. [D-P] E.B. Davies - M.M. Pang, The Cauchy problem and a generalization of the Hille-Yosida Theorem, Proc. London Math. Soc.55 (1987), 181-208. Zbl0651.47026MR887288
8. [deL1] R. Delaubenfels, Entire solutions of the abstract Cauchy problem, Semigroup Forum42 (1991), 83-105. Zbl0746.47018MR1075197
9. [deL2] R. Delaubenfels, C-semigroups and the Cauchy problem, J. Funct. Anal., to appear. Zbl0895.47029MR1200635
10. [deL3] R. Delaubenfels, Existence and uniqueness families for the abstract Cauchy problem, Proc. London Math. Soc., to appear. Zbl0766.47011MR1136443
11. [deL4] R. Delaubenfels, C-semigroups and strongly continuous semigroups, Preprint 1991. MR1231189
12. [deL5] R. Delaubenfels, Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvent, Preprint 1991. MR1223706
13. [Fr] A. Friedman, Generalized Functions and Partial Differential Equations, Prentice Hall, 1963. Zbl0116.07002MR165388
14. [H-N] B. Hennig - F. Neubrander, On representations, inversions and approximations of Laplace transforms in Banach spaces, Appl. Math. Ser., to appear. Zbl0791.44002MR1289741
15. [Hi1] M. Hieber, Integrated semigroups and differential operators in Lp spaces, Math. Ann.291 (1991), 1-16. Zbl0724.34067MR1125004
16. [Hi2] M. Hieber, Integrated semigroups and the Cauchy Problem for systems in Lp spaces, J. Math. Anal. Appl.162 (1991), 300-308. Zbl0766.47014MR1135280
17. [H-R] M. Hieber - F. Räbiger, A remark on the abstract Cauchy problem on spaces of Hölder continuous functions, Proc. Amer. Math. Soc., 115, n. 2, (1992), 431-434. Zbl0765.34042MR1092921
18. [Hö] L. Hörmander, Estimates for translation invariant operators in Lp spaces, Acta Math.104 (1960), 93-140. Zbl0093.11402MR121655
19. [Kr] H.O. Kreiss, Über sachgemässe Cauchyprobleme, Math. Scand.13 (1963), 109-128. Zbl0145.13303MR168921
20. [Lu] G. Lumer, Generalized evolution operators and (generalized) C-semigroups, in: Semigroup theory and Evolution. Ph. Clément, E. Mitidieri, B. de Pagter, (eds.). Lecture Notes in Pure and Appl. Math., Marcel Dekker, 135, (1991), 337-345. Zbl0748.47037MR1164660
21. [Mi] I. Miyadera, A generalization of the Hille-Yosida theorem, Proc. Japan Acad. Ser. A Math. Sci.64 (1988), 223-227. Zbl0683.47027MR974078
22. [M-T] I. Miyadera - N. Tanaka, A remark on exponentially bounded C-semigroups, Proc. Japan Acad. Ser. A Math. Sci.66 (1990), 31-34. Zbl0731.47040MR1051847
23. [Ne1] F. Neubrander, Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math.135 (1988), 111-155. Zbl0675.47030MR965688
24. [Ne2] F. Neubrander, Integrated semigroups and their application to complete second order problems, Semigroup Forum38 (1989), 233-251. Zbl0686.47038MR976206
25. [Pa] M.M.H. Pang, Resolvent estimates for Schrödinger operators in Lp(Rn) and the theory of exponentially bounded C-semigroups, Semigroup Forum41 (1990), 97-114. Zbl0739.47017MR1048325
26. [Paz] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. Zbl0516.47023MR710486
27. [Pe] I.G. Petrovskii, Über das Cauchysche Problem für ein System linearer partieller Differentialgleichungen im Gebiete der nichtanalytischen Funktionen, Bulletin de L'Université d'État de Moscou, Vol. I (7) (1938), 1-75. Zbl0024.03702JFM64.1156.02
28. [St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, New Jersey, 1970. Zbl0207.13501MR290095
29. [Ta] N. Tanaka, Holomorphic C-semigroups and holomorphic semigroups, Semigroup Forum38 (1989), 253-263. Zbl0651.47028MR976207
30. [T-O] N. Tanaka - N. Okazawa, Local C-semigroups and local integrated semigroups, Proc. London Math. Soc.61 (1990), 63-90. Zbl0703.47031MR1051099
31. [Tr] H. Triebel, Spaces of Besov-Hardy-Sobolev Type, Teubner, Leibzig, 1978. Zbl0408.46024MR581907