Eigenfunctions and eigenvalues of Fourier Transform?

[eljose]

I have a question..yesterday at Wikipedia i heard about the "Hermite Polynomials2 as Eigenfunctions of Fourier (complex?) transform with Eigenvalues i^{n} and i^{-n}...could someone explain what it refers with that?...when it says "Eigenfunctions-values" it refers to the Kernel K(x,t) that is a complex exponential function?...

 

[HallsofIvy]

In Linear Algebra, an "eigenvalue" and "eigenvector" of a linear transformation, L, are a number, $\lambda$, and vector, v, such that $Av= \lambda v$. We can think of the set of (integrable) functions as a vector space and the Fourier transform is a linear transformation on that set. The Hermite Polynomials have the property that the Fourier transform of the nth Hermite Polynomial, H_n, is
F(H_n)= iⁿH_n.

 

[mathman]

Note to Halls of Ivy. You left out the eigenvalue in your definition equation.

 

[HallsofIvy]

Note to Halls of Ivy. You left out the eigenvalue in your definition equation.

Thanks, I've edited it.

 

[HallsofIvy]

Note to Halls of Ivy. You left out the eigenvalue in your definition equation.

Thanks, I've edited it. (I misspelled "lamba" in the TEX)