Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eigenfunctions and eigenvalues of Fourier Transform?

  1. Jul 11, 2006 #1
    :rolleyes: :grumpy: :cool: 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?...
     
  2. jcsd
  3. Jul 11, 2006 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    In Linear Algebra, an "eigenvalue" and "eigenvector" of a linear transformation, L, are a number, [itex]\lambda[/itex], and vector, v, such that [itex]Av= \lambda v[/itex]. 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, Hn, is
    F(Hn)= inHn.
     
    Last edited: Jul 12, 2006
  4. Jul 11, 2006 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Note to Halls of Ivy. You left out the eigenvalue in your definition equation.
     
  5. Jul 12, 2006 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Thanks, I've edited it.
     
  6. Jul 12, 2006 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Thanks, I've edited it. (I misspelled "lamba" in the TEX)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Eigenfunctions and eigenvalues of Fourier Transform?
  1. Fourier transforms (Replies: 2)

  2. Fourier transformation (Replies: 0)

  3. Fourier transform (Replies: 2)

  4. Fourier transforms (Replies: 1)

  5. Fourier transform (Replies: 1)

Loading...