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Strongly continuous \(M,N\)-families of bounded operators. (English) Zbl 0802.47048

Summary: Corresponding to the strong wellposedness of the Cauchy problems for complete second order linear differential equations in Banach spaces, we introduce a notion of strongly continuous \(M,N\)-families and establish some basic results for these operator families.

MSC:

47E05 General theory of ordinary differential operators
47D09 Operator sine and cosine functions and higher-order Cauchy problems
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