Goerlich, E.; Pontzen, D. Approximation of operator semigroups of Oharu’s class \((C_{(k)})\). (English) Zbl 0498.47016 Tohoku Math. J., II. Ser. 34, 539-552 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 2 Documents 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 Keywords:operator semigroups; stability of difference schemes; continuous Trotter theorem on approximation of a (C0)-semigroup by a sequence of semigroups; discretization of a certain Cauchy problem; saturation for (C(k))- semigroups Citations:Zbl 0281.47024 PDFBibTeX XMLCite \textit{E. Goerlich} and \textit{D. Pontzen}, Tôhoku Math. J. (2) 34, 539--552 (1982; Zbl 0498.47016) Full Text: DOI References: [1] M. BECKER, Uber den Satz von Trotter mit Anwendungen auf die Approximationstheorie, Forsch. Bericht des Landes NRW Nr. 2577, Westdeutscher Verlag, 1976. [2] H. BERENS, Interpolationsmethoden zur Behandlung von Approximationsprozessen au Banachraumen, Lecture Notes in Mathematics 64, Springer-Verlag, Berlin-Heidelberg-New York, 1968. · Zbl 0164.43801 · doi:10.1007/BFb0077256 [3] P. BRENNER, V. THOMEE AND L. B. WAHLBIN, Besov Spaces and Applications to Differenc Methods for Initial Value Problems, Lecture Notes in Mathematics 434, Springer-Verlag, Berlin-Heidelberg-New York, 1975. · Zbl 0294.35002 [4] P. L. BUTZER AND H. BERENS, Semi-Groups of Operators and Approximation, Grundlehre der mathem. Wissenschaften 145, Springer-Verlag, Berlin-Heidelberg-New York, 1967. · Zbl 0164.43702 [5] W. DAHMEN, Trigonometric approximation with exponential error orders, I. Construc tion of asymptotically optimal processes; Generalized de la Vallee Poussin sums, Math. Ann. 230 (1977), 57-74; II. Properties of asymptotically optimal processes; Impossibility of arbitrarily good error estimates, J. Math. Anal. Appl. 68 (1979), 118-129. · Zbl 0342.42002 · doi:10.1007/BF01420576 [6] W. DAHMEN AND E. GORLIGH, Best approximation with exponential orders and inter mediate spaces, Math. Z. 148 (1976), 7-21. · Zbl 0318.41022 · doi:10.1007/BF01187865 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.