### Abstract

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

Original language | English |
---|---|

Pages (from-to) | 4413-4435 |

Number of pages | 23 |

Journal | Mediterranean Journal of Mathematics |

Volume | 13 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

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### Keywords

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

### Cite this

*Mediterranean Journal of Mathematics*,

*13*(6), 4413-4435. https://doi.org/10.1007/s00009-016-0753-1

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*Mediterranean Journal of Mathematics*, vol. 13, no. 6, pp. 4413-4435. https://doi.org/10.1007/s00009-016-0753-1

**One-Sided Invertibility Criteria for Binomial Functional Operators with Shift and Slowly Oscillating Data.** / Karlovych, Oleksiy; Karlovich, Yuri I.; Lebre, Amarino B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - One-Sided Invertibility Criteria for Binomial Functional Operators with Shift and Slowly Oscillating Data

AU - Karlovych, Oleksiy

AU - Karlovich, Yuri I.

AU - Lebre, Amarino B.

N1 - Sem PDF conforme despacho. info:eu-repo/grantAgreement/FCT/5876/147204/PT# info:eu-repo/grantAgreement/FCT/5876/147208/PT# This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and UID/MAT/04721/2013 (Centro de Analise Funcional, Estruturas Lineares e Aplicacoes). Yuri I. Karlovich was also supported by the SEP-CONACYT Projects No. 168104 and No. 169496 (Mexico).

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let α be an orientation-preserving homeomorphism of [ 0 , ∞] onto itself with only two fixed points at 0 and ∞, whose restriction to R+= (0 , ∞) is a diffeomorphism, and let Uα be the corresponding isometric shift operator acting on the Lebesgue space Lp(R+) by the rule Uαf=(α′)1/p(f∘α). We prove criteria for the one-sided invertibility of the binomial functional operator aI- bUα on the spaces Lp(R+) , p∈ (1 , ∞) , under the assumptions that a, b and α′ are bounded and continuous on R+ and may have slowly oscillating discontinuities at 0 and ∞.

AB - Let α be an orientation-preserving homeomorphism of [ 0 , ∞] onto itself with only two fixed points at 0 and ∞, whose restriction to R+= (0 , ∞) is a diffeomorphism, and let Uα be the corresponding isometric shift operator acting on the Lebesgue space Lp(R+) by the rule Uαf=(α′)1/p(f∘α). We prove criteria for the one-sided invertibility of the binomial functional operator aI- bUα on the spaces Lp(R+) , p∈ (1 , ∞) , under the assumptions that a, b and α′ are bounded and continuous on R+ and may have slowly oscillating discontinuities at 0 and ∞.

KW - limit operator

KW - one-sided invertibility

KW - Orientation-preserving non-Carleman shift

KW - slowly oscillating function

UR - http://www.scopus.com/inward/record.url?scp=84974844200&partnerID=8YFLogxK

U2 - 10.1007/s00009-016-0753-1

DO - 10.1007/s00009-016-0753-1

M3 - Article

VL - 13

SP - 4413

EP - 4435

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 6

ER -