Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace Expansions and the Noncommutative Residue for Manifolds with
  Boundary   For a pseudodifferential boundary operator A of integer order \nu and class
zero (in the Boutet de Monvel calculus) on a compact n-dimensional manifold
with boundary, we consider the function Trace(AB^{-s}) where B is an auxiliary
system formed of the Dirichlet realization of a second order strongly elliptic
differential operator and an elliptic operator on the boundary.
  We prove that Trace(AB^{-s}) has a meromorphic extension to the complex plane
with poles at the half-integers s = (n+\nu-j)/2, j = 0,1,... (possibly double
for s<0), and we prove that its residue at zero equals the noncommutative
residue of A, as defined by Fedosov, Golse, Leichtnam, and Schrohe by a
different method.
  To achieve this, we establish a full asymptotic expansion of
Trace(A(B-\lambda)^{-k}) in powers of \lambda^{-j/2} and log-powers
\lambda^{-j/2} log \lambda, where the noncommutative residue equals the
coefficient of the highest log-power.
  There is a related expansion for Trace(A exp(-tB)).

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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat