Abstract
It is known that regular factorizations of the characteristic function of an operator describe its invariant subspaces. The case of a scalar characteristic function is considered. Some examples are given. The factorizations describing all chains of invariant subspaces containing a given subspace L are constructed by the factorization describing L. A representation of the regular factorization of a function is obtained in terms of factorizations of its inner and outer parts. Bibliography: 9 titles.
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Gamal', M.F. Regular Factorization of the Scalar Characteristic Function. Journal of Mathematical Sciences 115, 2100–2118 (2003). https://doi.org/10.1023/A:1022824502008
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DOI: https://doi.org/10.1023/A:1022824502008