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

Oleksiy Karlovych, Yuri I. Karlovich, Amarino B. Lebre

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 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 ∞.

Original languageEnglish
Pages (from-to)4413-4435
Number of pages23
JournalMediterranean Journal of Mathematics
Volume13
Issue number6
DOIs
Publication statusPublished - 1 Dec 2016

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Shift Operator
Lebesgue Space
Invertibility
Lp Spaces
Diffeomorphism
Homeomorphism
Isometric
Discontinuity
Fixed point
Restriction
Operator

Keywords

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

Cite this

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

In: Mediterranean Journal of Mathematics, Vol. 13, No. 6, 01.12.2016, p. 4413-4435.

Research output: Contribution to journalArticle

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