Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete Norm Preserving Extensions of Holomorphic Functions   We show that for every connected analytic subvariety $V$ there is a
pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic
function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two
analytic disks intersecting at one point, if every bounded scalar valued
holomorphic function extends isometrically to $\Omega$, then so does every
matrix-valued function. In the special case that $\Omega$ is the symmetrized
bidisk, we show that this cannot be done by finding a linear isometric
extension from the functions that vanish at one point.

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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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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: 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: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol