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Approximation of operator semigroups of Oharu’s class \((C_{(k)})\). (English) Zbl 0498.47016


MSC:

47D03 Groups and semigroups of linear operators
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
41A40 Saturation in approximation theory

Citations:

Zbl 0281.47024
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References:

[1] M. BECKER, Uber den Satz von Trotter mit Anwendungen auf die Approximationstheorie, Forsch. Bericht des Landes NRW Nr. 2577, Westdeutscher Verlag, 1976.
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[7] W. DAHMEN AND E. GORLICH, The characterization problem for best approximation wit exponential error orders and evaluation of entropy, Math. Nachr. 76 (1977), 163-179. · Zbl 0324.41006 · doi:10.1002/mana.19770760112
[8] E. GORLICH AND D. PONTZEN, On approximation by operator semi-groups of a genera type (to appear).
[9] E. HILLE AND R. S. PHILLIPS, Functional Analysis and Semi-Groups, Amer. Math. Soc Colloq. Publ. Vol. 31, Providence, R. I. 1957. · Zbl 0078.10004
[10] TH. G. KURTZ, Extensions of Trotter’s operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. · Zbl 0174.18401 · doi:10.1016/0022-1236(69)90031-7
[11] S. OHARU, Semigroups of linear operators in a Banach space, Publ. RIMS, Kyoto Univ 7 (1971/1972), 205-260. · Zbl 0234.47042 · doi:10.2977/prims/1195193542
[12] H. SUNOUCHI, Convergence of semi-discrete difference schemes of abstract Cauchy prob lems, Thoku Math. J. 22 (1970), 394-408. · Zbl 0204.16101 · doi:10.2748/tmj/1178242766
[13] T. TAKAHASHI AND S. OHARU, Approximation of operator semigroups in a Banach space, Thoku Math. J. 24 (1972), 505-528. · Zbl 0281.47024 · doi:10.2748/tmj/1178241442
[14] V. THOMEE, Stability theory for partial difference operators, SIAM Rev. 11 (1969), 152-195. JSTOR: · Zbl 0176.09101 · doi:10.1137/1011033
[15] H. F. TROTTER, Approximation of semigroups of operators, Pacific J. Math. 8 (1958), 887-919. · Zbl 0099.10302 · doi:10.2140/pjm.1958.8.887
[16] H. F. TROTTER, Approximation and perturbation of semigroups, in: Linear Operator and Approximation II, ed. P. L. Butzer and B. Sz.-Nagy, Proc. Oberwolfach, ISNM 25, Birkhauser, Basel, 1974, 3-21. · Zbl 0302.47031
[17] K. YOSIDA, Functional Analysis, Springer-Verlag, Berlin-Heidelberg-New York, 1974 · Zbl 0286.46002
[18] A. ZYGMUND, Trigonometric Series I, Cambridge Univ. Press, 1959 · Zbl 0085.05601
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