Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyponormal Toeplitz operators with non-harmonic symbol acting on the
  Bergman space   The Toeplitz operator acting on the Bergman space $A^{2}(\mathbb{D})$, with
symbol $\varphi$ is given by $T_{\varphi}f=P(\varphi f)$, where $P$ is the
projection from $L^{2}(\mathbb{D})$ onto the Bergman space. We present some
history on the study of hyponormal Toeplitz operators acting on
$A^{2}(\mathbb{D})$, as well as give results for when $\varphi$ is a
non-harmonic polynomial. We include a first investigation of Putnam's
inequality for hyponormal operators with non-analytic symbols. Particular
attention is given to unusual hyponormality behavior that arises due to the
extension of the class of allowed symbols.

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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc