Borel functional calculus
（重定向自Completeness relation）
In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope. Thus for instance if T is an operator, applying the squaring function s → s to T yields the operator T. Using the functional calculus for larger classes of functions, we can for example define rigorously the "square root" of the (negative) Laplacian operator −Δ or the exponential