We deal with a Cauchy problem involving continuous linear operators from a Banach space E into itself. We prove that if the operators are nilpotent and pairwise commuting, then the problem is well-posed in the space of all infinitely differentiable functions from $R^n+1$ into E whose derivatives are equi-bounded on each bounded subset of $R^n+1$.

Partial differential equations in Banach spaces involving nilpotent linear operators.

CHINNI', Antonia;CUBIOTTI, Paolo
1996-01-01

Abstract

We deal with a Cauchy problem involving continuous linear operators from a Banach space E into itself. We prove that if the operators are nilpotent and pairwise commuting, then the problem is well-posed in the space of all infinitely differentiable functions from $R^n+1$ into E whose derivatives are equi-bounded on each bounded subset of $R^n+1$.
1996
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1860863
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