Semigroup Forum

, Volume 80, Issue 1, pp 121–142

On fractional resolvent operator functions


    • Department of MathematicsSichuan University
  • Miao Li
    • Department of MathematicsSichuan University

DOI: 10.1007/s00233-009-9184-7

Cite this article as:
Chen, C. & Li, M. Semigroup Forum (2010) 80: 121. doi:10.1007/s00233-009-9184-7


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.


α-times resolvent families(α,β)-resolvent operator functionsGeneratorsAnalyticity criteria

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