Complex powers of nondensely defined operators. (English) Zbl 1289.47086

The main aim of the author is a construction of the complex power of closed operators, see his paper [Publ. Inst. Math., Nouv. Sér. 83(97), 15–25 (2008; Zbl 1261.47024)]. In particular, structural properties of nondensely defined operators are proved (Theorem 2.1) and compared to the corresponding properties of various types of operators in detail (Remark 2.2). Moreover, the properties of analytic semigroups of growth order \(r>0\) are studied within the context of the introduced complex powers. As another application, the author transfers certain results on mild solutions of the abstract Cauchy problem from [J. M. A. M. van Neerven and B. Straub, Houston J. Math. 24, No. 1, 137–171 (1998; Zbl 0932.15016)] to nondensely defined generators of fractionally integrated semigroups.


47D06 One-parameter semigroups and linear evolution equations
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