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One-sided invertibility of discrete operators and their applications
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
University of Autonoma Estado Morelos, Mexico.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)In: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 92, no 1, p. 39-73Article in journal (Refereed) Published
Abstract [en]

For p is an element of [1, infinity], we establish criteria for the one-sided invertibility of binomial discrete difference operators A = aI - bV on the space l(p) = l(p)(Z), where a, b is an element of l(infinity), I is the identity operator and the isometric shift operator V is given on functions f. lp by (Vf)(n) = f (n+ 1) for all n is an element of Z. Applying these criteria, we obtain criteria for the one-sided invertibility of binomial functional operators A = aI - bU(alpha) on the Lebesgue space L-p(R+) for every p is an element of [1, infinity], where a, b is an element of L-infinity (R+), a is an orientation-preserving bi-Lipschitz homeomorphism of [0, +infinity] onto itself with only two fixed points 0 and infinity, and U-alpha is the isometric weighted shift operator on L-p(R+) given by U(alpha)f = (alpha)(1/p)(f circle alpha). Applications of binomial discrete operators to interpolation theory are given.

Place, publisher, year, edition, pages
SPRINGER BASEL AG , 2018. Vol. 92, no 1, p. 39-73
Keywords [en]
One-sided and two-sided invertibility; Discrete operator; Functional operator; Bi-Lipschitz homeomorphism; Real interpolation
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-144551DOI: 10.1007/s00010-017-0522-7ISI: 000419962100004OAI: oai:DiVA.org:liu-144551DiVA, id: diva2:1178290
Note

Funding Agencies|Linkoping University Grant (Sweden); SEP-CONACYT Project (Mexico) [168104]

Available from: 2018-01-29 Created: 2018-01-29 Last updated: 2018-01-29

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CiteExportLink to record
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