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Continuous invertibility of minimal Sturm–Liouville operators in Lebesgue spaces

Published online by Cambridge University Press:  12 July 2007

R. C. Brown  and
J. Cook
R. C. Brown
Affiliation:
Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, AL 35487-0350, USA (dbrown@gp.as.ua.edu)
J. Cook
Affiliation:
Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, AL 35487-0350, USA (cook077@bama.ua.edu)
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Abstract

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Using a standard theory of differential operators in Lebesgue spaces, we re-prove and generalize some results of Chernyavskaya and Shuster, giving (mostly sufficient) conditions that minimal operators determined by expressions of the form −(ry′)′ + qy with domain and range in possibly different Lp spaces on intervals with at least one singular endpoint have bounded inverses.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 53 - 70
Copyright
Copyright © Royal Society of Edinburgh 2006