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 $R^n+1$.File in questo prodotto:
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Partial differential equations in Banach spaces involving nilpotent linear operators.pdf
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