Spectrality of ordinary differential operators

Arkadi Minkin

doi:10.1016/j.jmaa.2005.10.058

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arXiv · math/0409181

Spectrality of ordinary differential operators

Arkadi Minkin

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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.

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Arkadi Minkin. 2004-09-10. Spectrality of ordinary differential operators. https://doi.org/10.1016/j.jmaa.2005.10.058

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