Details

Autor(en) / Beteiligte

• Kenessey, Nicolas
• Wengenroth, Jochen

Titel

Composition operators with closed range for smooth injective symbols R → R d

Ist Teil von

• Journal of functional analysis, 2011-05, Vol.260 (10), p.2997-3006

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2011

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals

Beschreibungen/Notizen

• In 1998, Allan, Kakiko, OʼFarrell, and Watson proved a description of the closure (with respect to the uniform convergence of all derivatives on compact sets) of A ( ψ ) = { F ∘ ψ : F ∈ E ( R d ) } for a smooth injective symbol ψ : R → R d in terms of formal Taylor series. In that article it was conjectured that A ( ψ ) is closed if ψ is proper and has only critical points of finite order. In the present paper we first give a simple counterexample and then rectify the conjecture by adding a geometrical property for the curve ψ ( R ) . This yields a characterization of A ( ψ ) ¯ = A ( ψ ) .