Structured Invariant Spaces of Vector Valued Functions, Hermitian Forms and a Generalization of Iohvidov's Laws
Document Type
Article
Publication Date
1990
Abstract
Vector spaces of pairs of rational vector valued functions, which are (1) invariant under the generalized backward shift and (2) endowed with a sesquilinear form which is subject to a structural identity, are studied. It is shown that any matrix can be viewed as the “Gram” matrix of a suitably defined basis for such a space. This identification is used to show that a rule due to Iohvidov for evaluating the rank of certain subblocks of a Toeplitz (or Hankel) matrix is applicable to a wider class of matrices with (appropriately defined) displacement rank equal to two. Enroute, a theory of reproducing kernel spaces is developed for nondegenerate spaces of the type mentioned above.
Recommended Citation
D. Alpay and H. Dym. Structured invariant spaces of vector valued functions, hermitian forms and a generalization of Iohvidov's laws. In Linear Algebra and its Applications, vol. 137 (1990), pp. 137-181.
Peer Reviewed
1
Copyright
Elsevier
Comments
This article was originally published in Linear Algebra and its Applications, volume 137, in 1990. DOI: 10.1016/0024-3795(90)90137-2