Representation of functions in an invariant subspace with almost real spectrum

Krivosheeva, O.; Krivosheev, A.

doi:10.1090/spmj/1509

Representation of functions in an invariant subspace with almost real spectrum
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by O. A. Krivosheeva and A. S. Krivosheev
Translated by: E. Peller

St. Petersburg Math. J. 29 (2018), 603-641

DOI: https://doi.org/10.1090/spmj/1509

Published electronically: June 1, 2018

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Abstract:

The invariant subspaces with almost real spectrum are studied. By a method based on the Leont′ev interpolation function, a criterion of the fundamental principle is obtained for these spaces. This criterion only consists of a simple geometric condition on the local distribution of the points of the spectrum with multiplicities. A complete characterization is given for the space of coefficients of the series that represent functions in an invariant subspace.

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