Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shamir-Duduchava Factorization of Elliptic Symbols   This paper considers the factorization of elliptic symbols which can be
represented by matrix-valued functions. Our starting point is a
\textit{Fundamental Factorization Theorem}, due to Budjanu and Gohberg. We
critically examine the work of Shamir, together with some corrections and
improvements as proposed by Duduchava. As an integral part of this work, we
give a new and detailed proof that certain sub-algebras of the Wiener algebra
on the real line satisfy a sufficient condition for right standard
factorization. Moreover, assuming only the Fundamental Factorization Theorem,
we provide a complete proof of an important result from Shargorodsky, on the
factorization of an elliptic homogeneous matrix-valued function, useful in the
context of the inversion of elliptic systems of multidimensional singular
integral operators in a half-space.

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The categories of this paper are: funct-an
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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: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph