Annals of Functional Analysis

Local operators and a characterization of the Volterra operator

Janusz Matkowski

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Abstract

We consider locally defined operators of the form $D^{n}\circ K$ where $D$ is the operator of differentiation and $K$ maps the space of continuous functions into the space of $n$-times\ differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed.

Article information

Source
Ann. Funct. Anal., Volume 1, Number 1 (2010), 36-40.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900990

Digital Object Identifier
doi:10.15352/afa/1399900990

Mathematical Reviews number (MathSciNet)
MR2755456

Zentralblatt MATH identifier
1216.47091

Subjects
Primary: 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05]
Secondary: 47A67: Representation theory

Keywords
Nemytskij operator locally defined operator superposition operator Volterra operator differentiable functions analytic functions

Citation

Matkowski, Janusz. Local operators and a characterization of the Volterra operator. Ann. Funct. Anal. 1 (2010), no. 1, 36--40. doi:10.15352/afa/1399900990. https://projecteuclid.org/euclid.afa/1399900990


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References

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