Spectrality of ordinary differential operators

Abstract

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.

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

References in corpus (2)

• Interpolation of subspaces and applications to exponential bases
• Unconditional bases of invariant subspaces of a contraction with finite defects