Abstract

We study the convergence rate of biorthogonal series expansions of functions in systems of root functions of a wide class of even-order ordinary differential operators defined on a finite interval. These expansions are compared with the trigonometric Fourier series expansions of the same functions in the integral or uniform metric on an arbitrary interior compact set of the main interval as well as on the entire interval. We show the dependence of the equiconvergence rate of these expansions on the distance from the compact set to the boundary of the interval, on the coefficients of the differential operation, and on the existence of infinitely many associated functions in the system of root functions.

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 call

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.