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 . These were obtained instead by use of the classical Balakrishnan formula , [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.
Operator Theory: Advances and Applications
Lasiecka, I., & Triggiani, R. (2015). Domains of fractional powers of matrix-valued operators: A general approach. Operator Theory: Advances and Applications, 250, 297-309. Retrieved from https://digitalcommons.memphis.edu/facpubs/4544