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Mediterranean Journal of Mathematics

, Volume 13, Issue 6, pp 4413–4435 | Cite as

One-Sided Invertibility Criteria for Binomial Functional Operators with Shift and Slowly Oscillating Data

  • Alexei Yu. Karlovich
  • Yuri I. Karlovich
  • Amarino B. Lebre
Article

Abstract

Let \({\alpha}\) be an orientation-preserving homeomorphism of \({[0,\infty]}\) onto itself with only two fixed points at 0 and \({\infty}\), whose restriction to \({\mathbb{R}_+=(0,\infty)}\) is a diffeomorphism, and let \({U_\alpha}\) be the corresponding isometric shift operator acting on the Lebesgue space \({L^p(\mathbb{R}_+)}\) by the rule \({U_\alpha f=(\alpha')^{1/p}(f\circ\alpha)}\). We prove criteria for the one-sided invertibility of the binomial functional operator \({aI-bU_\alpha}\) on the spaces \({L^p(\mathbb{R}_+)}\), \({p\in(1,\infty)}\), under the assumptions that a, b and \({\alpha'}\) are bounded and continuous on \({\mathbb{R}_+}\) and may have slowly oscillating discontinuities at 0 and \({\infty}\).

Keywords

Orientation-preserving non-Carleman shift slowly oscillating function limit operator one-sided invertibility 

Mathematics Subject Classification

Primary 39B32 Secondary 47A10 47B38 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Centro de Matemática e Aplicações, Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaCaparicaPortugal
  2. 2.Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y AplicadasUniversidad Autónoma del Estado de MorelosCuernavacaMexico
  3. 3.Centro de Análise Funcional, Estruturas Lineares e Aplicações, Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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