Polynomials of generators of integrated semigroups

Author:
Ralph deLaubenfels

Journal:
Proc. Amer. Math. Soc. **107** (1989), 197-204

MSC:
Primary 47D05; Secondary 47A60

DOI:
https://doi.org/10.1090/S0002-9939-1989-0975637-7

MathSciNet review:
975637

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Abstract: We give general sufficient conditions on and , for to generate an exponentially bounded holomorphic -times integrated semigroup, where is a polynomial and is a linear operator on a Banach space. Corollaries include the following.

(1) If generates a strongly continuous group and is a polynomial of even degree with positive leading coefficient, then generates a strongly continuous holomorphic semigroup of angle . (2) If generates a strongly continuous holomorphic semigroup of angle and is an th degree polynomial with positive leading coefficient, with , then generates a strongly continuous holomorphic semigroup of angle . (3) If generates an exponentially bounded holomorphic -times integrated semigroup of angle , and and are as in (2), then generates an exponentially bounded holomorphic -times integrated semigroup of angle .

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0975637-7

Article copyright:
© Copyright 1989
American Mathematical Society