Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $AC(\sigma)$ operators   In this paper we present a new extension of the theory of well-bounded
operators to cover operators with complex spectrum. In previous work a new
concept of the class of absolutely continuous functions on a nonempty compact
subset $\sigma$ of the plane, denoted $AC(\sigma)$, was introduced. An
$\AC(\sigma)$ operator is one which admits a functional calculus for this
algebra of functions. The class of $AC(\sigma)$ operators includes all of the
well-bounded operators and trigonometrically well-bounded operators, as well as
all scalar-type spectral operators, but is strictly smaller than Berkson and
Gillespie's class of $AC$ operators. This paper develops the spectral
properties of $AC(\sigma)$ operators and surveys some of the problems which
remain in extending results from the theory of well-bounded operators.

20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th