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The underdetermined Cauchy problem in Banach spaces. (English) Zbl 0231.34052

MSC:
34G10 Linear differential equations in abstract spaces
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References:
[1] Balakrishnan, A. V.: Fractional powers of closed operators and the semigroups generated by them. Pacific Jour. Math.10, 419-439 (1960). · Zbl 0103.33502
[2] Chazarain, J.: Problèmes de Cauchy au sens des distributions vectorielles et applications. C. R. Acad. Sci. Paris266, 10-13 (1968). · Zbl 0153.45402
[3] Dunford, N., Schwartz, J. T.: Linear operators, part I. New York: Interscience 1957. · Zbl 0128.34803
[4] Fattorini, H. O., Radnitz, A.: The Cauchy problem with incomplete initial data in Banach spaces. Michigan Math. Jour.18, 291-320 (1971). · Zbl 0208.16802 · doi:10.1307/mmj/1029000736
[5] Krein, S. G.: Linear differential equations in Banach spaces (Russian). Moscow: Goztekhizdat 1967.
[6] Prokopenko, L. N.: On uniqueness of solutions of the Cauchy problem for operational differential equations, Dokl. Akad. Nauk. SSSR148, 1030-1033 (1963).
[7] Radnitz, A.: The incomplete Cauchy problem in Banach spaces. Ph. D. dissertation at the University of California, Los Angeles, 1970.
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