Interpolation properties associated with the second order abstract Cauchy problem. (English) Zbl 0807.47030
Summary: Let \(A\) be a closed linear operator on a Banach space \(X\). In this work we present some interpolation and extrapolation results for the well posed abstract Cauchy problem of second order; namely, if the second order abstract Cauchy problem is exponentially well posed on \(D(A^{k+1})\), \(k\in N\), then \(A\) is “sandwiched” by cosine function generators.
MSC:
| 47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
Keywords:
closed linear operator on a Banach space; interpolation and extrapolation results; well posed abstract Cauchy problem of second order; cosine function generatorsReferences:
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