Regularized semigroups and systems of linear partial differential equations

Hieber, M.; Holderrieth, A.; Neubrander, F.

Hieber, M. ; Holderrieth, A. ; Neubrander, F.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 3, pp. 363-379.

MR 1205405 | Zbl 0789.35075

@article{ASNSP_1992_4_19_3_363_0,
     author = {Hieber, M. and Holderrieth, A. and Neubrander, F.},
     title = {Regularized semigroups and systems of linear partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {363--379},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {3},
     year = {1992},
     zbl = {0789.35075},
     mrnumber = {1205405},
     language = {en},
     url = {archive.numdam.org/item/ASNSP_1992_4_19_3_363_0/}
}

Hieber, M.; Holderrieth, A.; Neubrander, F. Regularized semigroups and systems of linear partial differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 3, pp. 363-379. http://archive.numdam.org/item/ASNSP_1992_4_19_3_363_0/

Bibliographie

[Ar1] W. Arendt, Vector valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352. | MR 920499 | Zbl 0637.44001

[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. | MR 1164640 | Zbl 0762.47013

[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. | MR 1018871 | Zbl 0675.45017

[A-N-S] W. Arendt - F. Neubrander - U. Schlotterbeck, Interpolation of semigroups and integrated semigroups, Semigroup Forum, 45, n. 1, (1992), 26-37. | EuDML 135168 | MR 1161416 | Zbl 0782.47035

[DaP1] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-246. | MR 225199 | Zbl 0195.41001

[DaP2] G. Da Prato, Semigruppi di crescenza n, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 20 (1966), 753-782. | EuDML 83407 | Numdam | MR 222710 | Zbl 0198.16801

[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. | MR 887288 | Zbl 0651.47026

[deL1] R. Delaubenfels, Entire solutions of the abstract Cauchy problem, Semigroup Forum 42 (1991), 83-105. | EuDML 135067 | MR 1075197 | Zbl 0746.47018

[deL2] R. Delaubenfels, C-semigroups and the Cauchy problem, J. Funct. Anal., to appear. | MR 1200635 | Zbl 0895.47029

[deL3] R. Delaubenfels, Existence and uniqueness families for the abstract Cauchy problem, Proc. London Math. Soc., to appear. | MR 1136443 | Zbl 0766.47011

[deL4] R. Delaubenfels, C-semigroups and strongly continuous semigroups, Preprint 1991. | MR 1231189

[deL5] R. Delaubenfels, Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvent, Preprint 1991. | MR 1223706

[Fr] A. Friedman, Generalized Functions and Partial Differential Equations, Prentice Hall, 1963. | MR 165388 | Zbl 0116.07002

[H-N] B. Hennig - F. Neubrander, On representations, inversions and approximations of Laplace transforms in Banach spaces, Appl. Math. Ser., to appear. | MR 1289741 | Zbl 0791.44002

[Hi1] M. Hieber, Integrated semigroups and differential operators in Lp spaces, Math. Ann. 291 (1991), 1-16. | MR 1125004 | Zbl 0724.34067

[Hi2] M. Hieber, Integrated semigroups and the Cauchy Problem for systems in Lp spaces, J. Math. Anal. Appl. 162 (1991), 300-308. | MR 1135280 | Zbl 0766.47014

[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. | MR 1092921 | Zbl 0765.34042

[Hö] L. Hörmander, Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93-140. | MR 121655 | Zbl 0093.11402

[Kr] H.O. Kreiss, Über sachgemässe Cauchyprobleme, Math. Scand. 13 (1963), 109-128. | MR 168921 | Zbl 0145.13303

[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. | MR 1164660 | Zbl 0748.47037

[Mi] I. Miyadera, A generalization of the Hille-Yosida theorem, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), 223-227. | MR 974078 | Zbl 0683.47027

[M-T] I. Miyadera - N. Tanaka, A remark on exponentially bounded C-semigroups, Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), 31-34. | MR 1051847 | Zbl 0731.47040

[Ne1] F. Neubrander, Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math. 135 (1988), 111-155. | MR 965688 | Zbl 0675.47030

[Ne2] F. Neubrander, Integrated semigroups and their application to complete second order problems, Semigroup Forum 38 (1989), 233-251. | MR 976206 | Zbl 0686.47038

[Pa] M.M.H. Pang, Resolvent estimates for Schrödinger operators in Lp(Rn) and the theory of exponentially bounded C-semigroups, Semigroup Forum 41 (1990), 97-114. | MR 1048325 | Zbl 0739.47017

[Paz] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. | MR 710486 | Zbl 0516.47023

[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. | JFM 64.1156.02 | Zbl 0024.03702

[St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, New Jersey, 1970. | MR 290095 | Zbl 0207.13501

[Ta] N. Tanaka, Holomorphic C-semigroups and holomorphic semigroups, Semigroup Forum 38 (1989), 253-263. | MR 976207 | Zbl 0651.47028

[T-O] N. Tanaka - N. Okazawa, Local C-semigroups and local integrated semigroups, Proc. London Math. Soc. 61 (1990), 63-90. | MR 1051099 | Zbl 0703.47031

[Tr] H. Triebel, Spaces of Besov-Hardy-Sobolev Type, Teubner, Leibzig, 1978. | MR 581907 | Zbl 0408.46024