Functional calculus

In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral theory. Historically, the term was synonymous with the calculus of variations; the latter term remains in extensive use in physics and engineering texts, whereas functional calculus develops the subject further with more mathematically careful, formal, abstract and precise articulations. The older usage is still visible in the functional derivative, which is often called the variational derivative.

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