sectorial

Sectorial is an adjective derived from sector and used to describe things that pertain to or are restricted to a particular sector, division, or area. In general usage, it denotes specialization or activity confined to a specific field or part of a system, such as a sector of an economy or a sector of a circle.

In mathematics, sectorial appears in the term sectorial operator. A sectorial operator is a densely defined linear operator on a Banach space whose spectrum lies in a sector of the complex plane and for which the resolvent satisfies a growth bound outside a slightly larger sector. Sectorial operators are central to the theory of analytic semigroups and functional calculus, providing a framework for solving abstract evolution equations and for defining fractional powers of operators. A common example is the negative Laplacian on Lp spaces, which generates an analytic semigroup and is sectorial of a certain angle.

In economics and the social sciences, sectorial is used to describe analyses, policies, or data organized by economic sectors, such as manufacturing, services, or agriculture. Sectorial studies examine how phenomena differ across sectors or how sector-specific factors influence outcomes, enabling targeted policy design and economic modeling.

Outside of mathematics and economics, sectorial is a more widely used term to indicate confinement to a specific sector or domain, though its technical usage is most precise in functional analysis and related fields. See also sector and sectorial analysis.