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Keywords:
abstract Cauchy problems; moment sequences
Summary:
We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.
References:
[1] Arendt W.: Vector-valued Laplace transforms and Cauchy Problems. Israel J. Math. 59 (1987), 327-352. MR 0920499 | Zbl 0637.44001
[2] Arendt W., Batty C.J.K., Hieber M., Neubrander F.: Vector Valued Laplace Transforms and Cauchy Problems. Birkhäuser, Basel, 2001. MR 1886588 | Zbl 0978.34001
[3] Arendt W., El-Mennaoui O., Keyantuo V.: Local integrated semigroups: Evolution with jumps of regularity. J. Math. Anal. Appl. 186 (1994), 572-595. MR 1293012 | Zbl 0833.47034
[4] Cioranescu I.: Local convoluted semigroups. Lecture Notes in Pure and Applied Math., No. 168, Marcel Dekker, N.Y., 1995, pp.107-122. MR 1300422 | Zbl 0818.47038
[5] Cioranescu I., Lumer G.: Problèmes d'évolution régularisés par un noyau général $K(t)$. Formule de Duhamel, prolongements, théorèmes de génération. C.R. Acad. Sci. Paris, t. 319, Série I, 1994, 1273-1278. MR 1310670 | Zbl 0821.47032
[6] Cioranescu I., Lumer G.: On $K(t)$-convoluted semigroups. Pitman Research Notes in Mathematics 324, (1995), 86-93. MR 1417060 | Zbl 0828.34046
[7] Diestel J., Uhl J.J.: Vector Measures. Amer. Math. Soc., Providence, 1977. MR 0453964 | Zbl 0521.46035
[8] Hieber M.: Integrated semigroups and differential operators on $L^p$ spaces. Math. Ann. 291 (1991), 1-16. MR 1125004
[9] Müller C.: Charakterisierung von Momentenfolgen in Banachräumen. Thesis of Diploma, Kaiserslautern, 1996.
[10] Neubrander F., Bäumer B.: Laplace transformmethods for evolution equations. Conference del Seminario di Mathematica dell' Universitá di Bari 259 (1994), 27-60. MR 1385478
[11] Phillips R.S.: An inversion formula for Laplace transforms and semigroups of linear operators. Ann. Math. 59 (1954), 325-356. MR 0060730
[12] Vieten P.: Holomorphie und Laplace Transformation Banachraumwertiger Funktionen. PhD thesis, Shaker, Aachen, 1995.
[13] Widder D.V.: The Laplace Transform. Princeton University Press, Princeton, 1972. MR 0005923 | Zbl 0139.29504
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