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Everything about Eigenfunction
Mathematical function of a linear operator
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: EigenfunctionA 5-minute orientation
- Skim a recent paper: Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditionsInfluential work since 2022
- Pick up a classic book: High precision methods in eigenvalue problems and their applicationsThe most-reprinted book on the subject
- Read the landmark paper: On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudesCited 601 times
- Go sideways: Self-adjoint operatorA closely related topic
- Go sideways: Spectral theory of ordinary differential equationsA closely related topic
📖 Definitions
Noun A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue).
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes
An eigenfunction expansion method for the analysis of exponential decay curves
SPATIAL MODELING IN ECOLOGY: THE FLEXIBILITY OF EIGENFUNCTION SPATIAL ANALYSES
Particle Acceleration at Ultrarelativistic Shocks: An Eigenfunction Method
Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory
Eigenfunction Expansions Associated with Second-order Differential Equations, Part 1
Three-dimensional eigenfunction analysis of a crack in a piezoelectric material
Extracting decadal morphological behaviour from high-resolution, long-term bathymetric surveys along the Holland coast using eigenfunction analysis
🆕 Influential since 2022
Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditions
Eigenfunction-based solution for one-dimensional solid-liquid phase change heat transfer problems with advection
Multifidelity Surrogate Modeling Based on Analytical Eigenfunction Expansions
Eigenfunction Martingale Estimators for Interacting Particle Systems and Their Mean Field Limit
Hybrid boundary element and eigenfunction expansion method for wave trapping by a floating porous box near a rigid wall
📚 Books worth reading
High precision methods in eigenvalue problems and their applicationsL. D. Akulenko, Leonid D. Akulenko · 2004
Direct Eigen Control For Induction Machines And Synchronous MotorsJean Claude Alacoque · 2012
Eigenfunction expansions associated with second-order differential equationsE. C. Titchmarsh · 1946- 📕Lectures on Exponential Decay of Solutions of Second-Order Elliptic EquationsShmuel Agmon · 2014
The Construction of Spin EigenfunctionsRuben Pauncz · 2000
Hangzhou Lectures on Eigenfunctions of the LaplacianChristopher D. Sogge · 2014
Slow Viscous FlowsP. N. Shankar · 2007- 📕A numerical study of wave propagation in a confined mixing layer by Eigenfunction expansionsFang Q. Hu · 1993
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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