Vol. 30, No. 2, 1969

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Concerning the infinite differentiability of semigroup motions

J. W. Spellmann

Vol. 30 (1969), No. 2, 519–523
Abstract

Let S be a real Banach space. Let C denote the infinitesimal generator of a strongly continuous semigroup T of bounded linear transformations on S. This paper presents a construction which proves that for each b > 1 there is a dense subset D(b) of S so that if p is in D(b), then

(A) p is in the domain of Cn for all positive integers n and

(B) limn→∞Cnp(n!)b = 0.

Condition (B) will be used in §3 to obtain series solutions to the partial differential equations U12 = CU and U11 = CU.

Mathematical Subject Classification
Primary: 47.50
Milestones
Received: 1 August 1968
Published: 1 August 1969
Authors
J. W. Spellmann