Local operators and a characterization of the Volterra operator
We consider locally defined operators of the form [D.sub.n] o 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...
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| Published in | Annals of functional analysis Vol. 1; no. 1; pp. 36 - 40 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Springer
01.01.2010
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| Online Access | Get full text |
| ISSN | 2008-8752 2008-8752 |
| DOI | 10.15352/afa/1399900990 |
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| Abstract | We consider locally defined operators of the form [D.sub.n] o 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. 2010 Mathematics Subject Classification. Primary 47H30; Secondary 47A67. Key words and phrases. Nemytskij operator, locally defined operator, superposition operator, Volterra operator, differentiable functions, analytic functions. |
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| AbstractList | We consider locally defined operators of the form [D.sub.n] o 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. 2010 Mathematics Subject Classification. Primary 47H30; Secondary 47A67. Key words and phrases. Nemytskij operator, locally defined operator, superposition operator, Volterra operator, differentiable functions, analytic functions. |
| Audience | Academic |
| Author | Matkowski, Janusz |
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