Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abrahamse's Theorem for matrix-valued symbols and subnormal Toeplitz
  completions   This paper deals with subnormality of Toeplitz operators with matrix-valued
symbols and, in particular, with an appropriate reformulation of Halmos's
Problem 5: Which subnormal Toeplitz operators with matrix-valued symbols are
either normal or analytic? In 1976, M. Abrahamse showed that if $\varphi\in
L^\infty$ is such that $\varphi$ or $\overline\varphi$ is of bounded type and
if $T_\varphi$ is subnormal, then $T_\varphi$ is either normal or analytic. In
this paper we establish a matrix-valued version of Abrahamse's Theorem and then
apply this result to solve the following Toeplitz completion problem: Find the
unspecified Toeplitz entries of the partial block Toeplitz matrix $$
A:=\begin{bmatrix} T_{\overline b_\alpha} & ?\\?& T_{\overline
b_\beta}\end{bmatrix}\quad\hbox{($\alpha,\beta\in\mathbb D$)} $$ so that $A$
becomes subnormal, where $b_\lambda$ is a Blaschke factor of the form
$b_\lambda(z):=\frac{z-\lambda}{1-\overline \lambda z}$ ($\lambda\in \mathbb
D$).

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol