Spectrality of ordinary differential operators

Details Spectrality of ordinary differential operators Spectrality of ordinary differential operators

2004-09-10

arxiv.org/abs/math/0409181v2

J. Math. Anal. Appl. 323 (2006) 387-402

Mathematics

Spectral Theory

AmsLaTeX, 26 pages, added section on dissipative operators and references

Scientific paper

10.1016/j.jmaa.2005.10.058

We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford's spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein's conjecture that dissipative differential operators are Birkhoff-regular and give sharp estimate of the norms of spectral projectors in the odd case. Considerations are based on a new direct method, exploiting \textit{almost orthogonality} of Birkhoff's solutions of the equation $l(y)=\lambda y$, which was discovered earlier by the author.

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