eigenfunctions's Usage Examples:

subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

solutions are the eigenfunctions associated to each λ.

This terminology is because the solutions correspond to the eigenvalues and eigenfunctions of a Hermitian.

When f and g are eigenfunctions for the same eigenvalue, then d d x W ( f , g ) = 0 , {\displaystyle.

For all LTI systems, the eigenfunctions, and the basis functions of the transforms, are complex exponentials.

The analysis of these problems involves the eigenfunctions of a differential operator.

Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes.

The complex-valued eigenfunctions of any linear time-invariant (LTI) system are of the following forms:.

Its eigenfunctions are | ϕ ⟩ {\displaystyle |\phi \rangle \,} and its eigenvalues are the.

particularly useful for understanding non-normal operators and their eigenfunctions.

map is an exactly solvable model of deterministic chaos, in that the eigenfunctions and eigenvalues of the transfer operator can be explicitly determined.

If one chooses the eigenfunctions of the position operator as a set of basis functions, one speaks of.

In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere.

 b] consisting of eigenfunctions of TK such that the corresponding sequence of eigenvalues {λi}i is nonnegative.

The eigenfunctions corresponding to non-zero.

is an orthonormal basis of the Hilbert space L2 that consists of the eigenfunctions of the autocovariance operator.

Explicit formulas for all the eigenfunctions can now be found by repeated application of a † {\displaystyle a^{\dagger.

This is sometimes also called the homogeneity operator, because its eigenfunctions are the monomials in z: θ ( z k ) = k z k , k = 0 , 1 , 2 , … {\displaystyle.

} Let φn denote the associated eigenfunctions, normalized to be orthonormal in L2(U).

functions for a semisimple Lie group G also provide a set of simultaneous eigenfunctions for the natural action of the centre of the universal enveloping algebra.

Riemannian manifolds and especially the asymptotic and distribution of its eigenfunctions (e.