Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Failure of Approximation of Odd Functions by Odd Polynomials   We construct a Hilbert holomorphic function space $H$ on the unit disk such
that the polynomials are dense in $H$, but the odd polynomials are not dense in
the odd functions in $H$. As a consequence, there exists a function $f$ in $H$
that lies outside the closed linear span of its Taylor partial sums $s_n(f)$,
so it cannot be approximated by any triangular summability method applied to
the $s_n(f)$. We also show that there exists a function $f$ in $H$ that lies
outside the closed linear span of its radial dilates $f_r, ~r<1$.

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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat