Domains of fractional powers of matrix-valued operators: A general approach


We present a general approach for identifying explicitly domains of fractional powers of matrix-valued operators. Such strategy will be illustrated by revisiting the topic of domains of fractional powers of ‘strongly damped’ abstract elastic equations, and recovering in this case established results [10]. These were obtained instead by use of the classical Balakrishnan formula [3], [21, p. 69], which is based on knowledge of the resolvent operator. A virtue of the present approach – which results evident in the present illustrative case – is that it is more conceptual and less computationally intensive than the former approach. In particular, it is resolvent independent.

Publication Title

Operator Theory: Advances and Applications

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