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Everything about Functional calculus
Theory allowing one to apply mathematical functions to mathematical operators
In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch of the field of functional analysis, connected with spectral theory. Historically, the term was synonymous with the calculus of variations; the latter term remains in extensive use in physics and engineering texts, whereas functional calculus develops the subject further with more mathematically careful, formal, abstract and precise articulations. The older usage is still visible in the functional derivative, which is often called the variational derivative. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Functional calculusA 5-minute orientation
- Skim a recent paper: Axially Harmonic Functions and the Harmonic Functional Calculus on the S-spectrumInfluential work since 2022
- Pick up a classic book: A Course of Pure MathematicsThe most-reprinted book on the subject
- Read the landmark paper: Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force FieldsCited 22,851 times
- Go sideways: Borel functional calculusA closely related topic
- Go sideways: Composition operatorA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
Fractional Calculus via Functional Calculus: Theory and Applications
Functional Itô calculus
The Functional Calculus
The Weyl functional calculus
Malliavin calculus and Euclidean quantum mechanics. I. Functional calculus
Functional calculus for noncommuting operators.
🆕 Influential since 2022
Axially Harmonic Functions and the Harmonic Functional Calculus on the S-spectrum
Properties of a polyanalytic functional calculus on the S ‐spectrum
The Verse Calculus: A Core Calculus for Deterministic Functional Logic Programming
The harmonic $H^{\infty}$-functional calculus based on the $S$-spectrum
Hadamard functional integral operators within fractional multiplicative calculus
📚 Books worth reading
A Course of Pure MathematicsG. H. Hardy, T. W. Körner · 1908
PrecalculusRon Larson, Roland E. Larson · 1900
CalculusRon Larson · 1988
Introduction to Infinitesimal Analysis: Functions of One Real VariableVeblen, Oswald, Nels Johann Lennes · 1907
Calculus, Early TranscendentalsJames Stewart · 1991
The integration of functions of a single variableG. H. Hardy, J. G. Leathem · 1905
CalculusJames Stewart · 1986
CalculusBruce H. Edwards, Ron Larson · 1900
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Generalizations of the derivative In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical…
- Jordan normal form [⌜λ11⌝λ11⌞λ1⌟⌜λ21⌝⌞λ2⌟[λ3]⋱⌜λn1⌝⌞λn⌟] Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known…
- 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…
- Holomorphic functional calculus In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a…
- Differential operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator (which is an operation that accepts a function…
- Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as a1x1+⋯+anxn=b, linear maps such as the following: (x1,…,xn)↦a1x1+⋯+anxn…