Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Densely Defined Multiplication on the Sobolev Space   Following Sarason's classification of the densely defined multiplication
operators over the Hardy space, we classify the densely defined multipliers
over the Sobolev space, $W^{1,2}[0,1]$. In this paper we find that the
collection of such multipliers for the Sobolev space is exactly the Sobolev
space itself. This sharpens a result of Shields concerning bounded multipliers.
The densely defined multiplication operators over the subspace $W_0 = \{f \in
W^{1,2}[0,1] : f(0)=f(1)=0 \}$ are also classified. In this case the densely
defined multiplication operators can be written as a ratio of functions in
$W_0$ where the denominator is non-vanishing. This is proved using a
contructive argument.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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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: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: econ