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

Borel functional calculus is more general than the continuous functional calculus, and its focus is different than the holomorphic functional calculus. More...

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

the continuous functional calculus, and then pass to measurable functions via the Riesz–Markov–Kakutani representation theorem. For the continuous functional...

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

for the measurable functional calculus, just as the norm topology does for the continuous functional calculus. The linear functionals on the set of bounded...

would often want to include order relations, formulas involving continuous functional calculus, and spectral data as relations. For that reason, we use a relatively...

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

(functional analysis) Friedrichs extension Stone's theorem on one-parameter unitary groups Stone–von Neumann theorem Functional calculus Continuous functional...

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

the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are...

modern usage) Ghiloni, R.; Moretti, V.; Perotti, A. (2013). "Continuous slice functional calculus in quaternionic Hilbert spaces". Rev. Math. Phys. 25 (4):...

In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete...

integration sums a function f(x) over a continuous range of values of x, functional integration sums a functional G[f], which can be thought of as a "function...

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

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

differential and integral equations. The usage of the word functional as a noun goes back to the calculus of variations, implying a function whose argument is...

generating functions. During this period, calculus techniques were applied to approximate discrete problems by continuous ones. In the 18th century, Euler introduced...

or almost every point. Early in the history of calculus, many mathematicians assumed that a continuous function was differentiable at most points. Under...

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...

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...

principal square root is continuous on this set of matrices. These properties are consequences of the holomorphic functional calculus applied to matrices....

V=\left(\bigoplus _{\alpha \in A}T_{z}\right)\oplus U.} So we invoke the continuous functional calculus f → f(U), and define Φ : C ∗ ( S ) → C ∗ ( V ) by Φ ( T f +...

of type − × X {\displaystyle -\times X} on objects; In functional programming and lambda calculus, function types are used to express the idea of higher-order...

self-adjoint operator are obtained by the continuous functional calculus.) The trace is a linear functional over the space of trace-class operators, that...

provide a semantics for lambda calculus (as ordinary set theory is inadequate to do this). More generally, Scott-continuous functions are now studied in...

version of singular value decomposition. By property of the continuous functional calculus, |A| is in the C*-algebra generated by A. A similar but weaker...

version of singular value decomposition. By property of the continuous functional calculus, |A| is in the C*-algebra generated by A. A similar but weaker...

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

ISBN 978-3-540-26653-2. Shreve, Steven E. (2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer Science+Business Media. ISBN 978-0-387-40101-0...