- 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}}}...
- is an
orthonormal basis of the
Hilbert space L2 that
consists of the
eigenfunctions of the
autocovariance operator. FPCA
represents functional data in the...
- Heath-Brown (1986)
Eigenfunction Expansions ****ociated with Second-order
Differential Equations. Part I (1946) 2nd.
edition (1962);
Eigenfunction Expansions ****ociated...
- 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 ,...
-
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...
- an
infinite number of
eigenvalues each with a
unique eigenfunction, and that
these eigenfunctions form an
orthonormal basis of a
certain Hilbert space...
- The
overtones of a
vibrating string are
eigenfunctions of the
second derivative, and form a
harmonic progression. The ****ociated
eigenvalues form the arithmetic...
