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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
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
Copyright
Copyright © Royal Society of Edinburgh 2006