Semigroup Forum

, Volume 42, Issue 1, pp 83–105

Entire solutions of the abstract cauchy problem

  • Ralph deLaubenfels
Research Article

DOI: 10.1007/BF02573409

Cite this article as:
deLaubenfels, R. Semigroup Forum (1991) 42: 83. doi:10.1007/BF02573409


We introduce a family of operators that we will callentire C-groups, and apply them to the first and second order abstract Cauchy problem, for a large class of linear operators on a Banach space. This produces unique solutions, for all initial data in a large (often dense) set, eachof which extends to an entire function, with continuous dependence on the initial data.

Applications include the backward heat equation and the Cauchy problem for the Laplace equation.

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Ralph deLaubenfels
    • 1
  1. 1.Department of MathematicsOhio UniversityAthens