Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of local unconditional structure in spaces of smooth functions
  on the torus of arbitrary dimension   Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators
with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space of
smooth functions generated by this collection, namely, the space of functions
$f$ such that $T_j f \in C(\mathbb{T}^n)$, $1\leq j\leq J$. We prove that if
there are at least two linearly independent operators among their senior parts
(relative to some mixed pattern of homogeneity), then this space does not have
local unconditional structure. This fact generalizes the previously known
result that such spaces are not isomorphic to a complemented subspace of $C(S)$

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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex