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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

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    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 by a moderator: Jul 12, 2006
  4. Jul 11, 2006 #3

    mathman

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

    HallsofIvy

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

    HallsofIvy

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