Abstract
SynopsisCertain classical differential expressions which are singular at a finite end-point (or at an interior point) can be represented as regular, scalar quasi-differential expressions, the best-known examples being the Boyd Equation and Laplace Tidal Wave Equation. We show here that in all such cases the domains of the minimal and maximal operators in the appropriate weighted Hilbert space, for the regularised expression, coincide with the corresponding domains for the expression in its original, singular form.This is contrasted with a known property of the corresponding expression domains. Whereas for an expressionM, the operator domains contain only functions y for which bothyandMylie in the appropriate Hilbert space, the expression domain comprises a much larger set of functions with no such restrictions beyond those necessary forMyto exist as a function. In the second-order case, the expression domain of the regularisation of a singular expression is known to be a strict subset of the original expression domain, contrasting with the results proved here for the operator domains.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
