Fractional Powers Non-Negative Operators Almost Sectorial Operators Functional Calculus Semigroups of Operators 47A60 47D06
Issue Date:
2005
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 8, No 2, (2005), 201p-230p
Abstract:
In this paper, we extend the theory of complex powers of operators to a
class of operators in Banach spaces whose spectrum lies in C \ ]−∞, 0[ and
whose resolvent satisfies an estimate ||(λ + A)^(−1)|| ≤ (λ^(−1) + λ^m)
M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators
strictly contains the class of the non negative operators and the one of
operators with polynomially bounded resolvent. We also prove that this
theory may be extended to sequentially complete locally convex spaces.
