In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately...

In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative...

operator theory and C*-algebra theory, the continuous functional calculus is a functional calculus which allows the application of a continuous function...

In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a...

The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

the above describes the Koopman operator as it appears in Borel functional calculus. The domain of a composition operator can be taken more narrowly...

require the following properties of this functional calculus: Φ extends the polynomial functional calculus. The spectral mapping theorem holds: σ(f(T))...

in mathematics for his the "Causal functional calculus", a calculus for non-anticipative, or "causal", functionals on the space of paths. Cont and collaborators...

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...

Stone–von Neumann theorem Functional calculus Continuous functional calculus Borel functional calculus Hilbert–Pólya conjecture Lp space Hardy space Sobolev...

eigenvectors". One application of the spectral theorem is to define a functional calculus. That is, if f {\displaystyle f} is a function on the real line and...

eigenvalues. A similar technique works more generally with the holomorphic functional calculus, using A − 1 = Q Λ − 1 Q − 1 {\displaystyle \mathbf {A} ^{-1}=\mathbf...

Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such...

In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and...

lambda calculus, which extended the lambda calculus by assigning a data type to all terms. This forms the basis for statically typed functional programming...

Functional Calculus of First Order Based on Strict Implication" (JSL, 1946), and "The Identity of Individuals in a Strict Functional Calculus of Second...

typed lambda calculus (⁠ λ → {\displaystyle \lambda ^{\to }} ⁠), a form of type theory, is a typed interpretation of the lambda calculus with only one...

Borel functional calculus gives additional ways to break up the spectrum naturally. This subsection briefly sketches the development of this calculus. The...

in σ(T). Any spectral theorem can be reformulated in terms of a functional calculus. In the present context, we have: Theorem. Let C(σ(T)) denote the...

finite-difference calculus, a discrete analogue of "calculus" Functional calculus, a way to apply various types of functions to operators Schubert calculus, a branch...

of matrices. These properties are consequences of the holomorphic functional calculus applied to matrices. The existence and uniqueness of the principal...

spaces. Functional calculus historically the term was used synonymously with calculus of variations, but now refers to a branch of functional analysis...

the spectral theorem (in whatever form) is the idea of defining a functional calculus. That is, given a function f {\displaystyle f} defined on the spectrum...

(A*A)1/2 is the unique positive square root of A*A given by the usual functional calculus. So by the lemma, we have A = U ( A ∗ A ) 1 2 {\displaystyle A=U(A^{*}A)^{\frac...

lambda calculus a special case with only one type. Typed lambda calculi are foundational programming languages and are the base of typed functional programming...

operators, a functional calculus is required. In the case of the exponential function, the continuous, or just the holomorphic functional calculus suffices...

the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a...

continuous on the spectrum of a {\displaystyle a} , the continuous functional calculus defines a self-adjoint element f ( a ) {\displaystyle f(a)} . Let...

dimension of the singular set for minimisers of the Mumford-Shah functional", Calculus of Variations and Partial Differential Equations, 16 (2): 187–215...

differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the...