Page 1

Displaying 1 – 5 of 5

Showing per page

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

Ralph deLaubenfels (1992)

Studia Mathematica

Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup e - s A s 0 such that ( 1 / s 2 ) e - s A s > 0 is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup e - s A s 0 and ∃ M < ∞ such that H n ( s ) ( k = 0 n ( s k A k ) / k ! ) e - s A M , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup e - z A R e ( z ) > 0 that is O(|z|) in all...

Currently displaying 1 – 5 of 5

Page 1