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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.
Upload file; Special pages ... Download as PDF; ... Wikidata item; Appearance. move to sidebar hide. This is a list of functional analysis topics. See also: Glossary ...
The simplest example of a reproducing kernel Hilbert space is the space (,) where is a set and is the counting measure on . For x ∈ X {\displaystyle x\in X} , the reproducing kernel K x {\displaystyle K_{x}} is the indicator function of the one point set { x } ⊂ X {\displaystyle \{x\}\subset X} .
Add the following into the article's bibliography * {{Swartz An Introduction to Functional Analysis}} and then add a citation by using the markup
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators.The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators.
[6] Peter Lax remarked that it "contained everything known, and many things not yet known, on linear functional analysis." [ 4 ] : 6 Béla Sz.-Nagy wrote in a review of the first volume: "the authors have created an extraordinarily important and valuable work that is distinguished in particular by its monumental completeness, clear organization ...
Functional data analysis (FDA) is a branch of statistics that analyses data providing information about curves, surfaces or anything else varying over a continuum. In its most general form, under an FDA framework, each sample element of functional data is considered to be a random function.
In functional analysis, a state of an operator system is a positive linear functional of norm 1. States in functional analysis generalize the notion of density matrices in quantum mechanics, which represent quantum states, both mixed states and pure states. Density matrices in turn generalize state vectors, which only represent pure states.