Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A homeomorphism theorem for sums of translates   For a fixed positive integer $n$ consider continuous functions $K_1,\dots$, $
K_n:[-1,1]\to \mathbb{R}\cup\{-\infty\}$ that are concave and real valued on
$[-1,0)$ and on $(0,1]$, and satisfy $K_j(0)=-\infty$. Moreover, let
$J:[0,1]\to \mathbb{R}\cup\{-\infty\}$ be such that $[0,1]\setminus
J^{-1}(\{-\infty\})$ has at least $n+1$ elements, but it is arbitrary
otherwise. For $x_0:=0<x_1<\dots< x_n \le x_{n+1}:=1$, so called nodes, and for
$t\in [0,1]$ consider the sum of translates function'
$F(x_1,\ldots,x_n,t):=J(t)+\sum_{j=1}^n K_j(t-x_j)$, and the vector of interval
maximum values $m_j:=m_j(x_1,\ldots,x_n):=\max_{t\in [x_j,x_{j+1}]} F$
($j=0,1,\ldots,n$). We describe the structure of the arising interval maxima as
the nodes run over the $n$-dimensional simplex. Applications presented here
range from abstract moving node Hermite--Fej\'er interpolation for generalized
algebraic and trigonometric polynomials via Bojanov's problem to more abstract
results of interpolation theoretic flavour. Finally, more subtle applications
concerning diverse minimax, equioscillation, maximin existence and
characterization results, are previewed, whose detailed description follows in
a forthcoming, companion paper.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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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: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an