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Everything about Differential operator
Typically linear operator defined in terms of differentiation of functions
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Differential operatorA 5-minute orientation
- Skim a recent paper: Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problemsInfluential work since 2022
- Pick up a classic book: Operational methods in applied mathematicsThe most-reprinted book on the subject
- Read the landmark paper: An iteration method for the solution of the eigenvalue problem of linear differential and integral operatorsCited 3,651 times
- Go sideways: D-moduleA closely related topic
- Go sideways: Pseudo-differential operatorA closely related topic
📖 Definitions
Noun An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives).
🏆 Landmark papers (most cited)
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
Integration of operator differential equations
Centralizers in differential, pseudo-differential and fractional differential operator rings
Primitivity in differential operator rings
Pseudo-Differential Operators Associated with the Jacobi Differential Operator
q-Differential operator identities and applications
An unsolvable hypoelliptic differential operator
New Differential Operator for Holomorphic Functions
🆕 Influential since 2022
Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems
Variational Physics-informed Neural Operator (VINO) for solving partial differential equations
Physics-Informed Neural Operator for Learning Partial Differential Equations
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Laplace neural operator for solving differential equations
📚 Books worth reading
Operational methods in applied mathematicsCarslaw, H. S. · 1941
Linear partial differential operatorsLars Hörmander · 1964
Lineĭnye different︠s︡ialʹnye operatoryM. A. Naĭmark · 1954
Nonlinear Perron-Frobenius theoryBas Lemmens · 2012
Elementary introduction to the theory of pseudodifferential operatorsXavier Saint Raymond · 1991
Linear Integral EquationsRam P. Kanwal · 2013- 📕Theory of nonlinear operatorsReinhard Kluge · 1977
- 📕Mimetic discretization methodsJosé E. Castillo · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- D-module In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of…
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