- 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...
- mathematics, a
Hecke eigensheaf is any
sheaf whose value is
based on an
eigenfunction. It is an
object that is a tensor-multiple of
itself when
formed under...
-
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...
- to
multiplication in the
frequency domain. For all LTI systems, the
eigenfunctions, and the
basis functions of the transforms, are
complex exponentials...
- an
infinite number of
eigenvalues each with a
unique eigenfunction, and that
these eigenfunctions form an
orthonormal basis of a
certain Hilbert space...
- {\tfrac {d}{dx}}} , in
which case the
eigenvectors are
functions called eigenfunctions that are
scaled by that
differential operator, such as d d x e λ x =...
