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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 016 854 409  
Author(s):  
Lomov, I. S.:  
Shorttitle:  
The local convergence of biorthogonal series related to differential operators with nonsmooth coefficients. II.  
Source:  
Differ. Equ. 37, 680  694 (2001); translation from Differ. Uravn. 37, No. 5, 648  660 (2001).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
nonselfadjoint ordinary linear differential operator of even order; set of the eigenfunctions and associated functions; biorthogonal set; partial sums of the biorthogonal series; partial sums of the Fourier trigonomertric series; equiconvergence estimates  
Review:  
Part II (or rather a technical appendix to part I) of a study of the so called equiconvergence which compares the biorthogonal expansions with trigonometric Fourier series. The former expansions are assumed generated by the root functions (i.e., eigenfunctions and the associated functions) of a certain nonselfadjoint ordinary differential operator L of order 2n. One, in particular, appreciates that the biorthogonal states need not by themselves be related to the adjoint operator (which even need not exist). The author gives the detailed proof of the key lemma on estimates on integrals, and formulates and proves the theorem on the basis property on local sets. On this background he in effect completes the proof of the equiconvergence rate theorem of part I.  
Remarks to the editors:  