* Factor ( functional analysis )

** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

On the advice of Cartan and Weil, he moved to the University of Nancy where he wrote his dissertation under Laurent Schwartz in functional analysis, from 1950 to 1953.

Grothendieck's early mathematical work was in functional analysis.

In a few years, he had turned himself into a leading authority on this area of functional analysis — to the extent that Dieudonné compares his impact in this field to that of Banach.

During this period significant analytical contributions to chemistry include the development of systematic elemental analysis by Justus von Liebig and systematized organic analysis based on the specific reactions of functional groups.

In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.

* barrelled space in functional analysis

From basic functional analysis we know that any ket can be written as

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

B *- algebras were mathematical structures studied in functional analysis.

In part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc.

C *- algebras ( pronounced " C-star ") are an important area of research in functional analysis, a branch of mathematics.

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

Consequently, the dual space is an important concept in the study of functional analysis.

He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

This approach has been successful and influential in relation with Hilbert's work in algebra and functional analysis, but has failed to engage in the same way with his interests in physics and logic.

Around 1909, Hilbert dedicated himself to the study of differential and integral equations ; his work had direct consequences for important parts of modern functional analysis.

Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators, that grew up around it during the 20th century.

In numerical analysis and functional analysis, a discrete wavelet transform ( DWT ) is any wavelet transform for which the wavelets are discretely sampled.

Koopman approached the study of ergodic systems by the use of functional analysis.

The Euler – MacLaurin formula can be understood as a curious application of some ideas from Banach spaces and functional analysis.

Felix Hausdorff ( November 8, 1868 – January 26, 1942 ) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.

However, the general concept of functional had previously been introduced in 1887 by the Italian mathematician and physicist Vito Volterra.

The concept of idempotence arises in a number of places in abstract algebra ( in particular, in the theory of projectors and closure operators ) and functional programming ( in which it is connected to the property of referential transparency ).

* Kent Applicative Operating System, a functional operating system concept

The Kent Applicative Operating System is a functional operating system concept to use dynamic process creation and inter-process communication.

RFT theorists introduced the concept of functional contextualism in language learning, which emphasizes the importance of predicting and influencing psychological events, such as thoughts, feelings, and behaviors, by focusing on manipulable variables in their context.

The concept of functional groups is central in organic chemistry, both as a means to classify structures and for predicting properties.

He borrowed the German word for ' environment ', Umwelt, to describe the individual's subjective world, and he invented the concept of functional circle ( Funktionskreis ) as a general model of sign processes.

The functional language Haskell restricts side effects with a static type system ; it uses the concept of monads to do stateful and IO computations .< ref > Imperative Functional Programming, Simon Peyton Jones and Phil Wadler, < em > Conference Record of the 20th Annual ACM Symposium on Principles of Programming Languages </ em >, pages 71 – 84, 1993 </ ref >

Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis.

The concept of the ignoble savage gave Europeans the " right " to establish colonies without considering the possibility of preexisting, functional societies.

In contrast to the model based on functional morphology described earlier, in the Epitheliozoa concept the ventral and dorsal cell layers of the Placozoa are homologs of endoderm and ectoderm, the two basic embryonic cell layers of the eumetazoans — the digestive gastrodermis in the Cnidaria or the gut epithelium in the bilaterally symmetrical Bilateria may have developed from endoderm, whereas ectoderm is, among other things, the precursor to the external skin layer ( epidermis ).

The concept of the solvation interaction can also be applied to an insoluble material, for example, solvation of functional groups on a surface of ion-exchange resin.

Organizationally, DIA adopted the concept of functional management to better address unified & specified command intelligence issues.

However, the concept of head transplantation may become more popular, as stem cells have been shown by the Wistar Institute of the University of Pennsylvania to repair the severed spinal cords of mice to a functional level.

Note that functional programming and distributed programming languages have a concept which is also called a protocol, but whose meaning is subtly different ( i. e. a specification of allowed exchanges of messages, emphasis on exchanges, not on messages ).

In functional analysis, the concept of an orthonormal basis can be generalized to arbitrary ( infinite-dimensional ) inner product spaces ( or pre-Hilbert spaces ).

:( 2 ) positioning, which is concept evaluation wherein concepts positioned in the same functional product class are evaluated together, and

Though he did not invent the concept, Wallis did much pioneering engineering work to make the swing-wing concept functional.

The concept of functional dependency arises when one attribute is dependent on another attribute and it also uniquely determines the other attribute.

This example illustrates the concept of functional dependency.

* Anamorphism, in computer science, is a concept from functional programming grounded in category theory