Summary
Using basic techniques from the theory of interpolation spaces equivalence theorems are established for the intermediate spaces between a given Banach space A and the domain D(Λr) of the r-th power of the infinitesimal generator Λ of a strongly continuous cosine operator function C. The results are applied to the study of second order evolution equations including regularity, order reduction and approximation by finite difference methods.
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Hoppe, R.H.W. Interpolation of cosine operator functions. Annali di Matematica pura ed applicata 136, 183–212 (1984). https://doi.org/10.1007/BF01773383
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DOI: https://doi.org/10.1007/BF01773383