Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions

J. Appell; Z. Jesús; O. Mejía

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 3, page 321-336
  • ISSN: 0392-4041

Abstract

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In this note we study the nonlinear composition operator f ↦ g ∘ f in various spaces of differentiable functions over an interval. It turns out that this operator is always bounded in the corresponding norm, whenever it maps such a space into itself, but continuous only in exceptional cases.

How to cite

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Appell, J., Jesús, Z., and Mejía, O.. "Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions." Bollettino dell'Unione Matematica Italiana 4.3 (2011): 321-336. <http://eudml.org/doc/290727>.

@article{Appell2011,
abstract = {In this note we study the nonlinear composition operator $f \mapsto g \circ f$ in various spaces of differentiable functions over an interval. It turns out that this operator is always bounded in the corresponding norm, whenever it maps such a space into itself, but continuous only in exceptional cases.},
author = {Appell, J., Jesús, Z., Mejía, O.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {321-336},
publisher = {Unione Matematica Italiana},
title = {Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions},
url = {http://eudml.org/doc/290727},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Appell, J.
AU - Jesús, Z.
AU - Mejía, O.
TI - Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/10//
PB - Unione Matematica Italiana
VL - 4
IS - 3
SP - 321
EP - 336
AB - In this note we study the nonlinear composition operator $f \mapsto g \circ f$ in various spaces of differentiable functions over an interval. It turns out that this operator is always bounded in the corresponding norm, whenever it maps such a space into itself, but continuous only in exceptional cases.
LA - eng
UR - http://eudml.org/doc/290727
ER -

References

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