Zentralblatt MATH - REVIEW SUBMISSION FORM

Zentralblatt MATH HOME

Your review has been received.

Thank you very much.

(You may want so save a copy of this page for your files.)

Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

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:

37L10

Normal forms, center manifold theory, bifurcation theory

47E05

Ordinary differential operators

Primary Classification:

46B15

Summability and bases

Secondary Classification:

40A05

Convergence and divergence of series and sequences

Keywords:

non-selfadjoint 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 bi-orthogonal
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
non-self-adjoint ordinary differential operator L of order 2n.
One, in particular, appreciates that the bi-orthogonal 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:

(New formular )