Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on BIBO Stability   The statements on the BIBO stability of continuous-time convolution systems
found in engineering textbooks are often either too vague (because of lack of
hypotheses) or mathematically incorrect. What is more troubling is that they
usually exclude the identity operator. The purpose of this note is to clarify
the issue while presenting some fixes. In particular, we show that a linear
shift-invariant system is BIBO-stable in the $L_\infty$-sense if and only if
its impulse response is included in the space of bounded Radon measures, which
is a superset of $L_1(\mathbb{R})$ (Lebesgue's space of absolutely integrable
functions). As we restrict the scope of this characterization to the
convolution operators whose impulse response is a measurable function, we
recover the classical statement.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th