Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Whitney type inequalities for local anisotropic polynomial
  approximation   We prove a multivariate Whitney type theorem for the local anisotropic
polynomial approximation in $L_p(Q)$ with $1\leq p\leq \infty$. Here $Q$ is a
$d$-parallelepiped in $\RR^d$ with sides parallel to the coordinate axes. We
consider the error of best approximation of a function $f$ by algebraic
polynomials of fixed degree at most $r_i - 1$ in variable $x_i,\ i=1,...,d$,
and relate it to a so-called total mixed modulus of smoothness appropriate to
characterizing the convergence rate of the approximation error. This theorem is
derived from a Johnen type theorem on equivalence between a certain
K-functional and the total mixed modulus of smoothness which is proved in the
present paper.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph