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Representation of fractional powers of infinitesimal generators of semigroups. (English) Zbl 0153.45203


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[1] A. V. Balakrishnan, An operational calculus for infinitesimal generators of semigroups., Trans. Amer. Math. Soc. 91 (1959), 330 – 353. · Zbl 0090.09701
[2] A. V. Balakrishnan, Fractional powers of closed operators and the semigroups generated by them, Pacific J. Math. 10 (1960), 419 – 437. · Zbl 0103.33502
[3] H. Berens and U. Westphal, Zur Charakterisierung von Ableitungen nichtganzer Ordnung im Rahmen der Laplacetransformation, Math. Nachr. (in press). · Zbl 0181.39401
[4] Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York Inc., New York, 1967. · Zbl 0164.43702
[5] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[6] Hikosaburo Komatsu, Fractional powers of operators, Pacific J. Math. 19 (1966), 285 – 346. · Zbl 0154.16104
[7] J.-L. Lions and J. Peetre, Sur une classe d’espaces d’interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5 – 68 (French). · Zbl 0148.11403
[8] U. Westphal, Charakterisierungen von Saturationsklassen für singulare Integrale vom Laplaceschen Faltungstyp, TH Aachen, 1966.
[9] K. Yosida, Functional analysis, Grundlehren d. math. Wiss. vol. 123, Springer, Berlin, 1965. · Zbl 0126.11504
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