Estimates of the Local Convergence Rate of Spectral Expansions for Even-Order Differential Operatorsстатья
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Аннотация:We study the convergence rate of biorthogonal series expansions of functions in
systems of root functions of a wide class of even-order ordinary di®erential operators de¯ned on
a ¯nite 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 coe±cients of the di®erential operation, and on the existence of in¯nitely many associated
functions in the system of root functions.