Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lieb-Thirring inequalities for higher order differential operators   We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of
order gamma >= 3/4 for fourth order Schr\"odinger operators in arbitrary
dimensions. We also consider some extensions to polyharmonic operators, and to
systems of such operators. For the critical case gamma = 1 - 1/2l in dimension
d=1 with differential order 2l >= 4 we prove the strict inequality
L^0(l,gamma,d) < L(l,gamma,d), which holds in contrast to current conjectures.

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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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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: cs
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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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: patt-sol