Everything about Functional analysis
Area of mathematics
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 and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Functional analysisA 5-minute orientation
- Skim a recent paper: The STRING database in 2023: protein–protein association networks and functional enrichment analyses for any sequenced genome of interestInfluential work since 2022
- Pick up a classic book: A course of modern analysisThe most-reprinted book on the subject
- Read the landmark paper: Functional AnalysisCited 1,056 times
- Go sideways: Vector-valued Hahn–Banach theoremsA closely related topic
- Go sideways: Banach spaceA closely related topic
📖 Definitions
Noun The branch of mathematics dealing with infinite-dimensional vector spaces, whose elements are actually functions, as well as generalizations such as Banach spaces and Hilbert spaces.
🏆 Landmark papers (most cited)
Functional Analysis
Functional Data Analysis
Functional analysis
Timing analysis using functional analysis
Functional Analysis Is Dead: Long Live Functional Analysis
Cartesian Functional Analysis
Functional Analysis
A functional analysis of a behavior analyst’s functional analysis
🆕 Influential since 2022
The STRING database in 2023: protein–protein association networks and functional enrichment analyses for any sequenced genome of interest
DAVID: a web server for functional enrichment analysis and functional annotation of gene lists (2021 update)
A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn
g:Profiler—interoperable web service for functional enrichment analysis and gene identifier mapping (2023 update)
📚 Books worth reading
A course of modern analysisE. T. Whittaker, G. N. Watson · 1902
PrecalculusRon Larson, Roland E. Larson · 1900
Problems and theorems in analysisGeorge Pólya, Gábor Szegő · 1925
CalculusJames Stewart · 1986
Elements of the theory of functions and functional analysis, by A.N. Kolmogorov and S.V. FominAndrei Nikolaevich Kolmogorov, Sergei Vasil'evic Fomin · 1957
Real AnalysisH. L. Royden, Patrick Fitzpatrick · 1963
Multivariable calculusJames Stewart · 1989
Complex AnalysisLars Valerian Ahlfors · 1953
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Vector-valued Hahn–Banach theorems In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach…
- Banach space In mathematics, more specifically in functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space…
- Hahn–Banach theorem In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace…
- List of functional analysis topics This is a list of functional analysis topics. See also: Glossary of functional analysis. Bra–ket notation Definite bilinear form Direct integral Euclidean…
- Glossary of functional analysis This is a glossary for the terminology in a mathematical field of functional analysis. Throughout the article, unless stated otherwise, the base field…
- Bounded operator In functional analysis and operator theory, a bounded linear operator is a special kind of linear transformation that is particularly important in infinite…
- Closed graph theorem (functional analysis) In mathematics, particularly in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological…
- Transpose of a linear map In linear algebra and functional analysis, the transpose or algebraic adjoint of a linear map between two vector spaces, defined over the same field, is…