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- W1993525714 abstract "There is a standard notion of type for a sectorial linear operator acting in a Banach space. We introduce a notion of asymptotic type for a linear operator V, involving estimates on the resolvent (λI+V)−1 as λ→0. We show, for example, that if V is sectorial and of asymptotic type ω then the fractional power Vα is of asymptotic type αω for a suitable range of positive α. Moreover, we establish various properties of the operator ∫01dαVα; in particular, this operator is of asymptotic type 0, for a sectorial operator V. This result has an application to the construction of operators satisfying the well-known Ritt resolvent condition." @default.
- W1993525714 created "2016-06-24" @default.
- W1993525714 creator A5020086820 @default.
- W1993525714 date "2009-03-01" @default.
- W1993525714 modified "2023-09-29" @default.
- W1993525714 title "Asymptotic type for sectorial operators and an integral of fractional powers" @default.
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- W1993525714 doi "https://doi.org/10.1016/j.jfa.2008.07.020" @default.
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