Abstract
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.
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Communicated by Jerome A. Goldstein
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deLaubenfels, R. Entire solutions of the abstract cauchy problem. Semigroup Forum 42, 83–105 (1991). https://doi.org/10.1007/BF02573409
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DOI: https://doi.org/10.1007/BF02573409