Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: U-cross Gram matrices and their invertibility   The Gram matrix is defined for Bessel sequences by combining synthesis with
subsequent analysis operators. If different sequences are used and an operator
U is inserted we reach so called U-cross Gram matrices. This can be seen as
reinterpretation of the matrix representation of operators using frames. In
this paper we investigate some necessary or sufficient conditions for Schatten
p-class properties and the invertibility of U-cross Gram matrices. In
particular, we show that under mild conditions the pseudo-inverse of a U-cross
Gram matrix can always be represented as a U-cross Gram matrix with dual frames
of the given ones. We link some properties of U-cross Gram matrices to
approximate duals. Finally, we state several stability results. More precisely,
it is shown that the invertibility of U-cross Gram matrices is preserved under
small perturbations.

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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol