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Kergin interpolation in Banach spaces

Henrik Petersson — 2002

Studia Mathematica

We study the Kergin operator on the space H N b ( E ) of nuclearly entire functions of bounded type on a Banach space E. We show that the Kergin operator is a projector with interpolating properties and that it preserves homogeneous solutions to homogeneous differential operators. Further, we show that the Kergin operator is uniquely determined by these properties. We give error estimates for approximating a function by its Kergin polynomial and show in this way that for any given bounded sequence of interpolation...

Rings of PDE-preserving operators on nuclearly entire functions

Henrik Petersson — 2004

Studia Mathematica

Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, N b ( E ) , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on N b ( E ) (i.e. the continuous operators that commute with all translations) is formed by the transposes φ ( D ) t φ , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on N b ( E ) is PDE-preserving for a set ℙ ⊆ Exp(F) if it...

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