Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernels of vector-valued Toeplitz operators   Let $S$ be the shift operator on the Hardy space $H^2$ and let $S^*$ be its
adjoint. A closed subspace $\FF$ of $H^2$ is said to be nearly $S^*$-invariant
if every element $f\in\FF$ with $f(0)=0$ satisfies $S^*f\in\FF$. In particular,
the kernels of Toeplitz operators are nearly $S^*$-invariant subspaces. Hitt
gave the description of these subspaces. They are of the form $\FF=g
(H^2\ominus u H^2)$ with $g\in H^2$ and $u$ inner, $u(0)=0$. A very particular
fact is that the operator of multiplication by $g$ acts as an isometry on
$H^2\ominus uH^2$. Sarason obtained a characterization of the functions $g$
which act isometrically on $H^2\ominus uH^2$. Hayashi obtained the link between
the symbol $\phii$ of a Toeplitz operator and the functions $g$ and $u$ to
ensure that a given subspace $\FF=gK_u$ is the kernel of $T_\phii$. Chalendar,
Chevrot and Partington studied the nearly $S^*$-invariant subspaces for
vector-valued functions. In this paper, we investigate the generalization of
Sarason's and Hayashi's results in the vector-valued context.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph