In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\displaystyle f} in that space that...

function such as x ↦ e i x , {\displaystyle x\mapsto e^{ix},} is an eigenfunction of the differential operator − i d d x {\displaystyle -i{\frac {d}{dx}}}...

Heath-Brown (1986) Eigenfunction Expansions Associated with Second-order Differential Equations. Part I (1946) 2nd. edition (1962); Eigenfunction Expansions Associated...

energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital...

(such as position, momentum, energy, angular momentum etc.). If ψ is an eigenfunction of the operator A ^ {\displaystyle {\hat {A}}} , then A ^ ψ = a ψ ,...

is an orthonormal basis of the Hilbert space L2 that consists of the eigenfunctions of the autocovariance operator. FPCA represents functional data in the...

an infinite number of eigenvalues each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space...

mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint...

where K is a continuous function symmetric in x and y. The resulting eigenfunction expansion expresses the function K as a series of the form K ( x , y...

modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional...