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On fractional resolvent operator functions. (English) Zbl 1185.47040
Summary: In this paper, we introduce three kinds of resolvent families defined by purely algebraic equations, which extend the classical semigroup property and cosine functional equation. We give their basic properties and analyticity criteria. Moreover, the relations between integrated resolvent families and resolvent families are discussed as well.

MSC:
47D03 Groups and semigroups of linear operators
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