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Representation formulas for cosine and sine functions of operators. II. (English) Zbl 0647.47048

Using a Korovkin type approximation theorem the authors give representation formulas for strongly continuous cosine and sine families of linear operators on Banach spaces. [For part I see ibid. 29, 162-171 (1985; Zbl 0591.47028).]
Reviewer: R.Nagel

MSC:

47D03 Groups and semigroups of linear operators
47D99 Groups and semigroups of linear operators, their generalizations and applications
41A36 Approximation by positive operators
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Citations:

Zbl 0591.47028
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References:

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[2] Lee, C.-S. andShaw, S.-Y.,Representation formulas for cosine and sine functions of operators. Aequationes Math.29 (1985), 162–172. · Zbl 0591.47028 · doi:10.1007/BF02189824
[3] Lutz, D.,An approximation theorem for cosine operator functions. C.R. Math. Rep. Acad. Sci. Canada4 (1982), 359–362. · Zbl 0514.47032
[4] Shaw, S.-Y.,Approximation of unbounded functions and applications to representations of semigroups. J. Approx. Theory28 (1980), 238–259. · Zbl 0452.41020 · doi:10.1016/0021-9045(80)90078-7
[5] Shaw, S.-Y.,Some exponential formulas for m-parameter semigroups. Bull. Inst. Math. Acad. Sinica9 (1981), 221–228. · Zbl 0467.47036
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[7] Webb, G. F.,A representation formula for strongly continuous cosine families. Aequationes Math.21 (1980), 251–256. · Zbl 0467.47037 · doi:10.1007/BF02189359
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