@article{CM_1970__22_1_67_0,
author = {Westphal, U.},
title = {Ein Kalk\"ul f\"ur gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren. Teil I : Halbgruppenerzeuger},
journal = {Compositio Mathematica},
volume = {22},
year = {1970},
pages = {67-103},
mrnumber = {261395},
zbl = {0194.15401},
language = {de},
url = {http://dml.mathdoc.fr/item/CM_1970__22_1_67_0}
}
Westphal, U. Ein Kalkül für gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren. Teil I : Halbgruppenerzeuger. Compositio Mathematica, Tome 22 (1970) pp. 67-103. http://gdmltest.u-ga.fr/item/CM_1970__22_1_67_0/
[1] An operational calculus for infinitesimal generators of semigroups. Trans. Amer. Math. Soc. 91 (1959), 330-353. | MR 107179 | Zbl 0090.09701
[2] Fractional powers of closed operators and the semigroups generated by them. Pacific J. Math. 10 (1960), 419-437. | Zbl 0103.33502
[3] Equivalent representations for the infinitesimal generator of higher orders in semi-group theory. Nederl. Akad. Wetensch. Indag. Math. 27 (1965), 497-512. | Zbl 0135.36701
[4] Interpolationsmethoden zur Behandlung von Approximationsprozessen auf Banachräumen. Lecture Notes in Mathematics, no. 64. Springer, Berlin 1968, 90S. | MR 239340 | Zbl 0164.43801
, [5] Representation of fractional powers of infinitesimal generators of semi-groups. Bull. Amer. Math. Soc. 74 (1968), 191-196. | MR 220096 | Zbl 0153.45203
[6] Zur Charakterisierung von Ableitungen nichtganzer Ordnung im Rahmen der Laplace-Transformation. Math. Nachr. 38 (1968), 115-129. | MR 233154 | Zbl 0181.39401
[7] Diffusion equation and stochastic processes. Proc. Nat. Acad. Sci. USA 35 (1949), 368-370. | Zbl 0033.06803
[8] Sur la théorie des demi-groupes et classes de saturation de certaines intégrales singulieres. C. R. Acad. Sci. Paris 243 (1956), 1473-1475. | Zbl 0072.13203
AND [9] Semi-groups of operators and approximation. Grundl. d. math. Wiss., Bd. 145. Springer, Berlin 1967, xi+318 pp. | MR 230022 | Zbl 0164.43702
UND [10] Zur Charakterisierung von Saturationsklassen in der Theorie der Fourierreihen. Tôhoku Math. J. 17 (1965), 29-54. | MR 184029 | Zbl 0131.06802
UND [11] Hilberttransformation, gebrochene Integration und Differentiation. Forschungsberichte des Landes Nordrhein-Westfalen, Nr. 1889. Köln 1967, 81S. | MR 236631 | Zbl 0165.46002
[12] Handbuch der Laplacetransformation, Bd. I. Birkhäuser, Basel 1950, 581S. | MR 43253 | Zbl 0040.05901
AND [13] Linear Operators. I. General Theory. Pure and Applied Mathematics, Vol. 7. New York 1958, xiv+858 pp. | MR 117523 | Zbl 0084.10402
[14] On a generalization of Marcel Riesz' potentials and the semi-groups generated by them. Comm. Sém. Math. Univ. Lund. Tome Supplémentaire (1952), 72-81. | Zbl 0048.08503
AND [15] Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. Vol. 31. Providence, R.I. 1957, xii+808 pp. | MR 89373 | Zbl 0078.10004
[16] Note on fractional powers of linear operators. Proc. Japan Acad. 36 (1960), 94-96. | Zbl 0097.31802
[17] Fractional powers of operators. Pacific J. Math. 19 (1966), 285-346. | MR 201985 | Zbl 0154.16104
[18] Fractional powers of operators. II. Interpolation spaces. Pacific J. Math. 21 (1967), 89-111. | MR 206716 | Zbl 0168.10702
[19] Théorèmes de trace et d'interpolation I. Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 389-403. | Numdam | Zbl 0097.09502
ET [20] Sur une classe d'espaces d'interpolation. Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5-68. | Numdam | MR 165343 | Zbl 0148.11403
[21] Sur les dérivees et sur les différences des fonctions de variables réelles. Journ. de Math. 6 (1927) 337-425. | JFM 53.0232.02
[22] A functional calculus using singular Laplace integrals. Trans. Amer. Math. Soc. 88 (1958), 400-413. | Zbl 0081.33501
[23] Über Potenzen von linearen Operatoren in Banachschen Räumen. Acta Sci. Math. (Szeged) 28 (1967), 107-121. | Zbl 0171.12203
[24] Nouvelles propriétés d'espaces d'interpolation. C. R. Acad. Sci. Paris 256 (1963), 1424-1426. | Zbl 0129.08401
[25] On the generation of semi-groups of linear operators. Pacific J. Math. 2 (1952), 343-369. | Zbl 0047.11004
[26] L'intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math. 81 (1948), 1-223. | MR 30102 | Zbl 0033.27601
[27] On one parameter groups of linear transformations I. Ann. of Math. 48 (1947), 216-233. | MR 20218 | Zbl 0038.16702
[28] Characterization of certain classes of functions. Töhoku Math. J.(2), 14 (1962), 127-134. | Zbl 0113.27503
et [29] Analyse harmonique des opérateurs de l'espace de Hilbert. Akadémiai Kiadó et Paris, Budapest 1967, xi +374 pp. | Zbl 0157.43201
[30] Charakterisierungen von Saturationsklassen für singuläre Integrale vom Laplaceschen Faltungstyp. TH Aachen 1966.
[31] Über Potenzen von Erzeugern von Halbgruppenoperatoren. In: Abstract spaces and approximation, herausgegeben von P. L. Butzer und B. Sz.-Nagy. Birkhäuser, Basel 1969. | MR 257815 | Zbl 0198.17601
[32] The Laplace transform. Princeton Mathematical Series, No. 6,1941, x+406 pp. | MR 5923 | Zbl 0063.08245
[33] Fractional powers of infinitesimal generators and the analyticity of the semigroups generated by them. Proc. Japan Acad. 36 (1960), 86-89. | MR 121665 | Zbl 0097.31801
[34] Functional analysis. Springer, Berlin 1965, xi+458 pp. | MR 180824 | Zbl 0126.11504
[35] Classes de saturation de certains procédés d'approximation des séries de Fourier des fonctions continues. Ann. Sci. École Norm. Sup. (3) 66 (1949), 19-93. | Numdam | Zbl 0034.18702